CBSE Class 11 Physics Work Energy And Power Worksheet

Work Energy and Power MCQ Questions with Answers Class 11 Physics Chapter 6

Question- A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10s, its energy is  1/8 mv₀² , the value of k will be : 

Question-  The extra force required to keep the belt moving is

Answer: D

Question- The magnitude of work done by a force
(a) depends on frame of reference
(b) does not depend on frame of reference
(c) cannot be calculated in non-inertial frames.
(d) both (a) and (b)

Answer: A

Question- Kinetic energy, with any reference, must be
(a) zero
(b) positive
(c) negative
(d) both (b) and (c)

Answer: B

Question- A boy carrying a box on his head is walking on a level road from one place to another is doing no work. This statement is
(a) correct
(b) incorrect
(c) partly correct
(d) cannot say

Answer: A

Question-In which of the following work is being not done?
(a) Shopping in the supermarket
(b) Standing with a basket of fruit on the head
(c) Climbing a tree
(d) Pushing a wheel barrow

Answer: B

Question-If a light body and heavy body have same kinetic energy,then which one has greater linear momentum?
(a) Lighter body
(b) Heavier body
(c) Both have same momentum
(d) Can’t be predicted

Answer: B

Question-A man pushes a wall and fails to displace it, he does
(a) negative work
(b) positive but not maximum work
(c) no work at all
(d) maximum positive work

Answer: C

Question-According to work-energy theorem, the work done by the net force on a particle is equal to the change in its
(a) kinetic energy
(b) potential energy
(c) linear momentum
(d) angular momentum

Answer: A

Question-Work is always done on a body when
(a) a force acts on it
(b) it moves through a certain distance
(c) it experiences an increase in energy through a mechanical influence
(d) None of these

Answer: C

Question-Total ....X.... energy of a system is conserved, if the forces, doing work on it, are .....Y..... .Here, X and Y refer to
(a) conservative, mechanical
(b) mechanical, conservative
(c) mechanical, non-conservative
(d) kinetic, conservative

Answer: B

Question-No work is done if
(a) displacement is zero
(b) force is zero
(c) force and displacement are mutually perpendicular
(d) All of these

Answer: D

Question- A bullet is fired and gets embedded in block kept on table. If table is frictionless, then
(a) kinetic energy gets conserved
(b) potential energy gets conserved
(c) momentum gets conserved
(d) both (a) and (c)

Answer: C

Question- Which of the following is not a conservative force?
(a) Gravitational force
(b) Frictional force
(c) Spring force
(d) None of these

Answer: B

Question-A light and a heavy body have equal momentum. Which one has greater K.E.?
(a) The lighter body
(b) The heavier body
(c) Both have equal K.E.
(d) Data given is incomplete

Answer: A

Question-When the force retards the motion of body, the work done is
(a) zero
(b) negative
(c) positive
(d) Positive or negative depending upon the magnitude of force and displacement

Answer: B

Question. A particle moves in the X–Y plane under the influence of a force F̅ such that its instantaneous momentum is p̅ = î2cost+ĵ2sint. What is the angle between the force and instantaneous momentum ?
(a) 0°
(b) 45°
(c) 90°
(d) 180°

Answer: C

Question. The bob A of a simple pendulum is released when the string makes an angle of 45º with the vertical. It hits another bob B of the same material and same mass kept at rest on the table. If the collision is elastic 
(a) both A and B rise to the same height
(b) both A and B come to rest at B
(c) both A and B move with the velocity of A
(d) A comes to rest and B moves with the velocity of A

Answer: D

Question. A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest
(a) at the highest position of the body
(b) at the instant just before the body hits the earth
(c) it remains constant all through
(d) at the instant just after the body is projected

Answer: B

Question. A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure correctly shown the displacementtime curve for its motion? 

Answer: B

Question. A particle of mass m1moving with velocity v strikes with a mass m2 at rest, then the condition for maximum transfer of kinetic energy is
(a) m₁ >> m₂
(b) m₂ >> m₂
(c) m₁ = m₂
(d) m1 = 2m²

Answer: C

Question. Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is
(a) 30 m/s
(b) 20 m/s
(c) 10 m/s
(d) 5 m/s

Answer: C

Question. A mass m is moving with velocity v collides inelastically with a bob of simple pendulum of mass m and gets embedded into it. The total height to which the masses will rise after collision is
(a) v²/8g
(b) v²/4g
(c) v²/2g
(d) 2v2/g

Answer: A

Question. A motor drives a body along a straight line with a constant force. The power P developed by the motor must vary with time t according to 

Answer: D

Question. A glass marble dropped from a certain height above the horizontal surface reaches the surface in time t and then continues to bounce up and down. The time in which the marble finally comes to rest is
(a) eⁿ t
(b) e²t
(c) t[1+e/1-e]
(d) t[1-e/1+e]

Answer: C

Question. A weight suspended from the free end of a vertically hanging spring produces an extension of 3 cm. The spring is cut into two parts so that the length of the longer part is 2/3 of the original length, If the same weight is now suspended from the longer part of the spring, the extension produced will be
(a) 0.1 cm
(b) 0.5 cm
(c) 1 cm
(d) 2 cm

Answer: D

Question. A particle, initially at rest on a frictionless horizontal surface, is acted upon by a horizontal force which is constant in magnitude and direction. A graph is plotted of the work done on the particle W, against the speed of the particle v.
If there are no other horizontal forces acting on the particle, the graph would look like 

Answer: C

Question. A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northwards with the same speed. If two particles coalesce on collision, the new particle of mass 2 m will move in the north-east direction with a velocity
(a) v / 2
(b) v √2
(c) v/ 2
(d) None of these

Answer: C

Question. A small block of mass m is kept on a rough inclined surface of inclination θ fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in time t as seen by the observer on the inclined p lane will be
(a) zero
(b) mgvt cos²θ
(c) mgvt sin² θ
(d) mgvt sin²θ

Answer: A

Question. A ramp is constructed in parabolic shape such that the height y of any point on its surface is given in terms of the point's horizontal distance x from the bottom of the ramp be y = x²/2L. A block of granite is to be set on the ramp; the coefficient of static friction is 0.80. What is the maximum x coordinate at which the block can be placed on the ramp and remain at rest, if L = 10 m? 
(a) 8 m
(b) 8.4 m
(c) 9 m
(d) 9.4 m

Answer: A

Question. The force F acting on a body moving in a circle of radius r is always perpendicular to the instantaneous velocity v. The work done by the force on the body in half rotation is
(a) Fv
(b) F·2pr
(c) Fr
(d) 0

Answer: D

Question. The negative of the distance rate of change of potential energy is equal to
(a) force acting on the particle in the direction of displacement
(b) acceleration of the particle, perpendicular to displacement
(c) power
(d) impulse.

Answer: A

Question. n small balls each of mass m impinge elastically each second on a surface with velocity v. The force experienced by the surface will be
(a) 1/2 mnv
(b) 2 mnv
(c) mnv
(d) 2 mnv

Answer: C

Question. A horse drinks water from a cubical container of side 1 m. The level of the stomach of horse is at 2 m from the ground. Assume that all the water drunk by the horse is at a level of 2m from the ground. Then minimum work done by the horse in drinking the entire water of the container is (Take ρ_water = 1000 kg/m3 and g = 10 m/s² )
(a) 10 kJ
(b) 15 kJ
(c) 20 kJ
(d) zero

Answer: D

Question. A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is 

Answer: A

Question. A body falls freely under gravity. Its velocity is v when it has lost potential energy equal to U. What is the mass of the body ?
(a) U²/v²
(b) 2U²/v²
(c) 2U/v²
(d) U /v²

Answer: C

Question. If a light body and heavy body have same kinetic energy, then which one has greater linear momentum?
(a) Lighter body
(b) Heavier body
(c) Both have same momentum
(d) Can’t be predicted

Answer: B

Question. The speed of an object of mass m dropped from an inclined plane (frictionless), at the bottom of the plane, depends on:
(a) height of the plane above the ground
(b) angle of inclination of the plane
(c) mass of the object
(d) All of these

Answer: A

Question. Work done by a conservative force is positive if
(a) P.E. of the body increases
(b) P.E. of the body decreases
(c) K.E. of the body increases
(d) K.E. of the body decreases

Answer: B

Question. Four particles given, have same momentum. Which has maximum kinetic energy
(a) Proton
(b) Electron
(c) Deutron
(d) α-particles

Answer: B

Question. Which of the following force(s) is/are non-conservative?
(a) Frictional force
(b) Spring force
(c) Elastic force
(d) All of these

Answer: A

Question. The ...X... energy V(x) of the spring is said to be zero when block and spring system is in the ...Y... position.Here, X and Y refer to
(a) potential, equilibrium
(b) kinetic, equilibrium
(c) mechanical, equilibrium
(d) vibrational, left

Answer: A

Question. Which of the diagrams shown in figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit? 

Answer: D

Question. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
(a) x
(b) ex
(c) x²
(d) loge x

Answer: C

Question. A body of mass 0.5 kg travels in a straight line with velocity v = a x^3/2 where a = 5 m–1/2s^–1. The work done by the net force during its displacement from x = 0 to x = 2 m is
(a) 15 J
(b) 50 J
(c) 10 J
(d) 100 J

Answer: B

Question. A particle of mass 10 kg moving eastwards with a speed 5 ms^–1 collides with another particle of the same mass moving north-wards with the same speed 5 ms^–1. The two particles coalesce on collision. The new particle of mass 20 kg will move in the north-east direction with velocity
(a) 10 ms^–1
(b) 5 ms^–1
(c) (5 /√2)ms^-1
(d) none of these

Answer: C

Question. A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is
(a) 140 J
(b) 100 J
(c) 60 J
(d) 40 J

Answer: C

Question. Two masses ma and mb moving with velocities va and vb in opposite direction collide elastically and after the collision ma and mb move with velocities Vb and Va respectively. Then the ratio ma/mb is
(a) Va - Vb/Va + Vb
(b) ma+mb/ma
(c) 1
(d) 1/2

Answer: C

Question. A rubber ball is dropped from a height of 5m on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of
(a) 16/25
(b) 2/5
(c) 3/5
(d) 9/25

Answer: B

Question. A 10 m long iron chain of linear mass density 0.8 kg m^–1 is hanging freely from a rigid support. If g = 10 ms^–2, then the power required to left the chain upto the point of support in 10 second
(a) 10 W
(b) 20W
(c) 30 W
(d) 40 W

Answer: D

Question. A 3 kg ball strikes a heavy rigid wall with a speed of 10 m/ s at an angle of 60º. It gets reflected with the same speed and angle as shown here. If the ball is in contact with the wall for 0.20s, what is the average force exerted on the ball by the wall? 

(a) 150 N
(b) Zero
(c) 150√3N
(d) 300 N

Answer: C

Question. A bomb of mass 1 kg is thrown vertically upwards with a speed of 100 m/s. After 5 seconds it explodes into two fragments.
One fragment of mass 400 gm is found to go down with a speed of 25 m/s. What will happen to the second fragment just after the explosion? (g = 10 m/s²)
(a) It will go upward with speed 40 m/s
(b) It will go upward with speed 100 m/s
(c) It will go upward with speed 60 m/s
(d) It will also go downward with speed 40m/s

Answer: B

Question. In a simple pendulum of length l the bob is pulled aside from its equilibrium position through an angle q and then released. The bob passes through the equilibrium position with speed
(a) √2gl(1+ cos θ)
(b) √2gl sin θ
(c) √2gl
(d) √2gl(1- cos θ)

Answer: D

Question. A stationary particle explodes into two particles of masses m₁ and m₂ which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E₂ is
(a) m₁v₂/m₂v₁
(b) m₂/m₁
(c) m₁/m₂
(d) 1

Answer: B

Question. Two particles A and B, move with constant velocities v̅₁ and v̅₂ . At the initial moment their position vectors are r̅₁ and r̅₂ respectively. The condition for particles A and B for their collision is: 

Answer: D

Question. An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms–1 and the second part of mass 2 kg moves with speed 8 ms^–1. If the third part flies off with speed 4 ms^–1 then its mass is
(a) 5 kg
(b) 7 kg 
(c) 17 kg
(d) 3 kg

Answer: A

Question. A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be
(a) 0.5 m
(b) 0.15 m
(c) 0.12 m
(d) 1.5m

Answer: B

Question. A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be
(a) 0, 1
(b) 1, 1
(c) 1, 0.5
(d) 0, 2

Answer: A

Question. If v be the instantaneous velocity of the body dropped from the top of a tower, when it is located at height h, then which of the following remains constant ?
(a) gh + v²
(b) gh + v²/2
(c) gh - v²/2
(d) gh – v²

Answer: B

Question. A nucleus moving with a velocity v̅ emits an α- particle. Let the velocities of the a-particle and the remaining nucleus be v̅₁ and v̅₂ and their masses be m₁ and m₂.
(a) v̅,v̅₁ and v̅₂ must be parallel to each other
(b) None of the two of v̅ , v̅₁ and v̅₂ should be parallel to each other.
(c) m₁ v̅₁ + m₂ v̅₂ must be parallel to (m₁+m₂)v̅.
(d) None of these

Answer: C

Question. A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t – 4t² + t³, where x is in metres and t is in seconds. The work done during the first 4 seconds is
(a) 576 mJ
(b) 450 mJ
(c) 490 mJ
(d) 530 mJ

Answer: A

Question. If the mass of the body is halved and velocity gets doubled then final kinetic energy would be .........of initial.
(a) same
(b) four times
(c) double
(d) eight times

Answer: C

Question.  If two particles are brought near one another, the potential energy of the system will
(a) increase
(b) decrease
(c) remains the same
(d) equal to the K.E

Answer: A

Question. A particle is taken round a circle by application of force. The work done by the force is
(a) positive non–zero
(b) negative non–zero
(c) Zero
(d) None of the above

Answer: C

Question. Which of the following is correct?
(a) W = FS cos θ
(b) P. E. = mgh
(c) K. E. =1/2 mv²
(d) All of these

Answer: D

Question. The potential energy of a system increases if work is done
(a) upon the system by a non conservative force
(b) by the system against a conservative force
(c) by the system against a non conservative force
(d) upon the system by a conservative force

Answer: D

Question. The total mechanical energy of a system is conserved if the force, doing work on it is
(a) constant
(b) variable
(c) conservative
(d) non-conservative

Answer: C

Question. Two bodies of different masses are moving with same kinetic energy. Then the ratio of their momenta is equal to the ratio of their
(a) masses
(b) square of masses
(c) square root of masses
(d) cube root of masses

Answer: C

Question. If stretch in a spring of force constant k is doubled then the ratio of elastic potential energy in the two cases will be
(a) 4 : 1
(b) 1 : 4
(c) 2 : 1
(d) 1 : 2

Answer: A

Question. The energy stored in wounded spring watch is
(a) Kinetic
(b) Potential
(c) Heat
(d) chemical

Answer: B

Question. The temperature at the bottom of a high water fall is higher than that at the top because
(a) by itself heat flows from higher to lower temperature
(b) the difference in height causes a difference in pressure
(c) thermal energy is transformed into mechanical energy
(d) mechanical energy is transformed into thermal energy.

Answer: D

Question. Law of conservation of energy states that
(a) work done is zero
(b) energy is zero
(c) work done is constant
(d) energy of world is constant

Answer: D

Question. The potential energy of a system increases if work is done
(a) upon the system by a non conservative force
(b) by the system against a conservative forc
(c) by the system against a non conservative force
(d) upon the system by a conservative force

Answer: D

Question-  When two bodies stick together after collision, the collision is said to be

(a) partially elastic

(b) elastic

(c) inelastic

(d) perfectly inelastic

Answer-(d)

Question-  If a force F is applied on a body and it moves with a velocity V, the power will be

(a) F×v

(b) F/v

(c) F/v²

(d) F×v²

Answer-(a)

Question-  Consider the elastic collision of two bodies A and B of equal mass. Initially B is at rest and A moves with velocity v. After the collision

(a) the body A traces its path back with the same speed

(b) the body A comes to rest and B moves away in the direction of A’s approach with the velocity v

(c) both the bodies stick together and are at rest

(d) B moves along with velocity v/2 and A retraces its path with velocity v/2.

Answer-(b)

Question- In an inelastic collision

(a) momentum is not conserved

(b) momentum is conserved but kinetic energy is not conserved

(c) both momentum and kinetic energy are conserved

(d) neither momentum nor kinetic energy is conserved

Answer-(b)

Question- Which of the following must be known in order to determine the power output of an automobile?

(a) Final velocity and height

(b) Mass and amount of work performed

(c) Force exerted and distance of motion

(d) Work performed and elapsed time of work

Answer-(d)

Question- The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact

(a) is extremely small

(b) is moderately small

(c) is extremely large

(d) depends on particular case

Answer-(a)

Question-  Which one of the following statements is true?

(a) Momentum is conserved in elastic collisions but not in inelastic collisions

(b) Total kinetic energy is conserved in elastic collisions but momentum is not conserved in elastic collisions

(c) Total kinetic energy is not conserved but momentum is conserved in inelastic collisions

(d) Kinetic energy and momentum both are conserved in all types of collisions

Answer-(c)

Question- In case of elastic collision, at the time of impact.

(a) total K.E. of colliding bodies is conserved.

(b) total K.E. of colliding bodies increases

(c) total K.E. of colliding bodies decreases

(d) total momentum of colliding bodies decreases.

Answer-(c)

Question-  In an inelastic collision, which of the following does not remain conserved?

(a) Momentum

(b) kinetic energy

(c) Total energy

(d) Neither momentum nor kinetic energy

Answer-(b)

Question- The coefficient of restitution e for a perfectly inelastic collision is

(a) 1

(b) 0

(c) ∞

(d) –1

Answer-(b)

Question- In a one-dimensional elastic collision, the relative velocity of approach before collision is equal to

(a) sum of the velocities of the bodies

(b) e times the relative velocity of separation after collision

(c) 1/e times the relative velocity of separation after collision

(d) relative velocity of separation after collision

Answer-(d)

Question-  If a shell fired from a cannon, explodes in mid air, then

(a) its total kinetic energy increases

(b) its total momentum increases

(c) its total momentum decreases

(d) None of these

Answer-(a)

Question- When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after collision they will move

(a) opposite to one another

(b) in the same direction

(c) together

(d) at right angle to each other

Answer-(d)

Question- The coefficient of restitution e for a perfectly elastic collision is

(a) 1

(b) 0

(c) ∞

(d) –1

Answer-(a)

Question- Unit of power is

(a) kilowatt hour

(b) kilowatt/hour

(c) watt

(d) erg

Answer-(c)

Question- When after collision the deformation is not relived and the two bodies move together after the collision, it is called

(a) elastic collision

(b) inelastic collision

(c) perfectly inelastic collision

(d) perfectly elastic collision

Answer-(c)

Question. A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision, their final velocities are V and v respectively. The value of v is
(a) 2uM/m
(b) 2um/M
(c) 2u/1+m/M
(d) 2u/1+M/m

Answer: C

Question. A shell is fired from a cannon with a velocity V at an angle q with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is
(a) 3 V cos θ
(b) 2 V cos θ
(c) 3/2 Vcos θ
(d) V cos θ

Answer: A

Question. An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is, because
(a) the two magnetic forces are equal and opposite, so they produce no net effect
(b) the magnetic forces do not work on each particle
(c) the magnetic forces do equal and opposite (but nonzero) work on each particle
(d) the magnetic forces are necessarily negligible

Answer: B

Question. A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a positron. In the same time t, the work done on the two moving charged particles is
(a) same as the same force law is involved in the two experiments
(b) less for the case of a positron, as the positron moves away more rapidly and the force on it weakens
(c) more for the case of a positron, as the positron moves away a larger distance
(d) same as the work done by charged particle on the stationary proton.

Answer: C

Question. The kinetic energy of particle moving along a circle of radius R depends upon the distance covered S and is given by K = aS where a is a constant. Then the force acting on the particle is
(a) aS/R
(b) 2(aS)²/R
(c) aS²/R²
(d) 2aS/R

Answer: D

Question. The potential energy of particle in a force field is U = A/r2 - B/r , where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is
(a) B / 2A
(b) 2A / B
(c) A / B
(d) B / A

Answer: B

Question. A body is falling freely under the action of gravity alone in vaccum. Which of the following quantities remain constant during the fall?
(a) Kinetic energy
(b) Potential energy
(c) Total mechanical energy
(d) Total linear momentum

Answer: C

Question. Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s².
The work done by the (i) gravitational force and the (ii) resistive force of air is 
(a) (i) 1.25 J (ii) –8.25 J
(b) (i) 100 J (ii) 8.75 J
(c) (i) 10 J (ii) – 8.75 J
(d) (i) – 10 J (ii) –8.25 J

Answer: C

Question. A particle of mass m is driven by a machine that delivers a constant power of k watts. If the particle starts from rest the force on the particle at time t is
(a) √mk t^–1/2
(b) √2mk t^–1/2
(c) 1/2√2mk t^–1/2
(d) √mk/2 t^–1/2

Answer: D

Question. During inelastic collision between two bodies, which of the following quantities always remain conserved?
(a) Total kinetic energy
(b) Total mechanical energy
(c) Total linear momentum
(d) Speed of each body

Answer: C

Question. Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in figure.
Which of the following statement is correct? 
(a) Both the stones reach the bottom at the same time but not with the same speed
(b) Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II
(c) Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I
(d) Both the stones reach the bottom at different times and with different speeds

Answer: C

Question. The ball rolls down without slipping (which is at rest at a) along ab having friction. It rolls to a maximum height h_c where bc has no friction. K_a, K_b and K_c are kinetic energies at a, b and c. Which of the following is correct ? 

(a) K_a = K_c, h_a = h_c
(b) K_b > K_c, h_a = h_c
(c) K_b > K_c, h_a < h_c
(d) K_b > K_c, h_a > hc

Answer: D

Question. A train of weight 10⁷ N is running on a level track with uniform speed of 36 km h^–1. The frictional force is 0.5 kg per quintal. If g = 10 m/s², then power of engine is
(a) 500 kW
(b) 50 kW
(c) 5 kW
(d) 0.5 kW

Answer: A

Question. The potential energy function for a particle executing linear SHM is given by V(x) = 1/2kx² where k is the force constant of the oscillator (Fig.). For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches x = ±x_m. If V and K indicate the PE and KE, respectively of the particle at x = +x_m, then which of the following is correct? 

(a) V = O, K = E
(b) V = E, K = O
(c) V < E, K = O
(d) V = O, K < E

Answer: B

Question. A raindrop falling from a height h above ground, attains a near terminal velocity when it has fallen through a height (3/4)h. Which of the diagrams shown in figure correctly shows the change in kinetic and potential energy of the drop during its fall up to the ground? 

Answer: B

Question. A uniform force of (3î + ĵ) newton acts on a particle of mass 2 kg. The particle is displaced from position (2î + k̂) meter to position (4î + 3ĵ - k̂) meter. The work done by the force on the particle is
(a) 6 J
(b) 13 J
(c) 15 J
(d) 9 J

Answer: D

Question. Which of the diagrams in figure correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient depth to impart it a terminal velocity? 

Answer: B

Question. The coefficient of friction between the tyres and the road is m. A car is moving with momentum p. What will be the stopping distance due to friction alone ? The mass of the
car is m.
(a) p²/2μg
(b) p²/2mμg
(c) p²/2m²μg
(d) p²/2mg

Answer: C

Question. If the kinetic energy of a body is increased by 300%, the momentum of the body is increased by
(a) 300%
(b) 200%
(c) 100%
(d) 50%

Answer: C

Question. A cricket ball of mass 150 g moving with a speed of 126 km/ h hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001s, the force that the batsman had to apply to hold the bat firmly at its place would be
(a) 10.5 N
(b) 21 N
(c) 1.05 × 10⁴ N
(d) 2.1 × 10⁴ N

Answer: C

Question. A uniform force of (3î + ĵ) newton acts on a particle of mass 2 kg. The particle is displaced from position ((2î + k̂) meter to position (4î + 3ĵ -k̂) meter. The work done by the force on the particle is
(a) 6 J
(b) 13 J
(c) 15 J
(d) 9 J

Answer: D

Question. A man squatting on the ground gets straight up and stand.
The force of reaction of ground on the man during the process is
(a) constant and equal to mg in magnitude
(b) constant and greater than mg in magnitude
(c) variable but always greater than mg
(d) at first greater than mg and later becomes equal to mg

Answer: D

Question. A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 ms^–1. The final velocity acquired by the person and the average force exerted on the person are 
(a) –1.6 ms^–1; 8 N
(b) –0.08 ms^–1; 16 N
(c) – 0.8 ms^–1; 8 N
(d) –1.6 ms^–1; 16 N

Answer: C

Question. A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when 
(a) U(x) > E
(b) U(x) < E
(c) U(x) = O 
(d) U(x) ≤ E

Answer: D

Question. One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio of 
(a) 1 : 2
(b) 1 : 3
(c) 2 : 1
(d) 3 : 1

Answer: A

Question. An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms^–1 and the second part of mass 2 kg moves with speed 8 ms^–1. If the third part flies off with speed 4 ms^–1 then its mass is
(a) 5 kg
(b) 7 kg
(c) 17 kg
(d) 3 kg

Answer: A

Question. In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 m s^–1 at 45° from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 m s^–2, the kinetic energy of the shotput when it just reaches the ground will be
(a) 2.5 J
(b) 5.0 J
(c) 52.5 J
(d) 155.0 J

Answer: D

Question. A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v).
The total kinetic energy generated due to explosion is :
(a) mv²
(b) 3/2 mv²
(c) 2 mv²
(d) 4 mv²

Answer: B

Question. A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 × 10^–4 J by the end of the second revolution after the beginning of the motion ? 
(a) 0.1 m/s²
(b) 0.15 m/s²
(c) 0.18 m/s²
(d) 0.2 m/s²

Answer: A

Question. Two similar springs P and Q have spring constants KP and K_Q, such that K_P > K_Q. They are stretched, first by the same amount (case a,) then by the same force (case b). The work done by the springs W_P and W_Q are related as, in case (a) and case (b), respectively
(a) W_P = W_Q ; W_P = W_Q
(b) W_P > W_Q ; W_Q > W_P
(c) W_P < W_Q ; W_Q < W_P
(d) WP = WQ ; WP > WQ

Answer: B

Question. A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200N and is directly opposed to the motion. The work done by the cycle on the road is
(a) + 2000 J
(b) – 200 J
(c) zero
(d) – 20,000 J

Answer: C

Question. The heart of man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 ×103 kg/m3 and g = 10m/s2 then the power of heart in watt is : 
(a) 2.35
(b) 3.0
(c) 1.50
(d) 1.70

Answer: D

Question. A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v₀ is : (Take g = 10 ms^–2)
(a) 20 ms^–1
(b) 28 ms^–1
(c) 10 ms^–1
(d) 14 ms^–1

Answer: A

Question. Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed v as shown in figure. 

If the collision is elastic, which of the following (figure) is a possible result after collision? 

Answer: B

Question. A mass of 5 kg is moving along a circular path of radius 1 m. If the mass moves with 300 rev/min, its kinetic energy would be
(a) 250 π²
(b) 100 π²
(c) 5 π²
(d) 0

Answer: A

Question. On a frictionless surface a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has a speed v/3 . The second block's speed after the collision is :
(a) 3/4 v
(b) 3/√2 v
(c) √3/2 v
(d) 2√2/3 v

Answer: D

Question. A block of mass 10 kg, moving in x direction with a constant speed of 10 ms–1, is subject to a retarding force F = 0.1 × J/m uring its travel from x = 20 m to 30 m. Its final KE will be:
(a) 450 J
(b) 275 J
(c) 250 J
(d) 475 J

Answer: D

Question. A body of mass 1 kg begins to move under the action of a time dependent force F̅ = (2tî + 3t2ĵ) N, where î and ĵ are unit vectors alogn x and y axis. What power will be developed by the force at the time t? 
(a) (2t² + 3t³)W
(b) (2t² + 4t⁴)W
(c) (2t³ + 3t⁴) W
(d) (2t³ + 3t⁵)W

Answer: D

DIRECTIONS : Each question contains Statement- 1 and Statement-2. Choose the correct answer from the following.
(a) Statement -1 is false, Statement-2 is true
(b) Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -1 is true, Statement-2 is false

Question. Statement -1 : A work done by friction is always negative.
Statement -2 : If frictional force acts on a body its K.E. may decrease.

Answer: A

Question. Statement -1 : An object of mass m is initially at rest. A constant force F acts on it. Then the velocity gained by the object during a fixed displacement is proportional to 1/√m.
Statement -2 : For a given force and displacement velocity is always inversely proportional to root of mass.

Answer: C

Question. Statement -1 : Mechanical energy is the sum of macroscopic kinetic & potential energies.
Statement - 2 : Mechanical energy is that part of total energy which always remain conserved.

Answer: D

Question. Statement-1 : A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical.
Statement -2 : The rate of change of momentum determines that the force is small or large.

Answer: B

Question. Statement -1 : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
Statement -2 : During collision intermolecular space decreases and hence elastic potential energy increases.

Answer: B