CBSE Class 11 Physics Motion In A Plane Worksheet

Motion In A Plane MCQ Questions with Answers Class 11 Physics

Question. What determines the nature of the path followed by a particle?
(a) Velocity
(b) Speed
(c) Acceleration
(d) None of these

Answer: C

Question. If θ is the angle between two vectors, then the resultant vector is maximum, when value of θ is
(a) 0°
(b) 90°
(c) 180°
(d) Same in all cases.

Answer: A

Question. A projectile is thrown horizontally with a speed of 20 ms^–1. If g is 10 ms^–2, then the speed of the projectile after 5 second will be nearly
(a) 0.5 ms^–1
(b) 5 ms^–1
(c) 54 ms^–1
(d) 500 ms^–1

Answer: C

Question. The velocity of a projectile at the initial point A is (2î + 3ĵ) m/s. It’s velocity (in m/s) at point B is 

Answer: B

Question. If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is : 
(a) 0°
(b) 90°
(c) 45°
(d) 180°

Answer: B

Question. A ball is projected at such an angle that the horizontal range is three times the maximum height. The angle of projection of the ball is
(a) sin^-1(3/4)
(b) sin^-1(4/3)
(c) cos^-1(4/3)
(d) tan^-1(4/3)

Answer: D

Question. A bucket, full of water is revolved in a vertical circle of radius 2 m. What should be the maximum time-period of revolution so that the water doesn’t fall out of the bucket?
(a) 1 sec
(b) 2 sec
(c) 3 sec
(d) 4 sec

Answer: C 

Question. A body is projected horizontally from a point above the ground and motion of the body is described by the equation x = 2t, y = 5t² where x, and y are horizontal and vertical coordinates in metre after time t. The initial velocity of the body will be
(a) √29 m/s horizontal
(b) 5 m/s horizontal
(c) 2 m/s vertical
(d) 2 m/s horizontal

Answer: D

Question. A vector P̅₁ is along the positive x-axis. If its vector product with another vector P̅₂ is zero then P̅₂ could be
(a) 4ĵ
(b) -4î
(c) (ĵ+k̂)
(d) -(î+ĵ)

Answer: B

Question. A wheel rotates with constant acceleration of 2.0 rod/s2, if the wheel starts from rest the number of revolutions it makes in the first ten seconds will be approximately
(a) 32
(b) 24
(c) 16
(d) 8

Answer: C

Question. A projectile thrown with a speed v at an angle θ has a range R on the surface of earth. For same v and q, its range on the surface of moon will be [gmoon = g Earth/6]
(a) R/6
(b) R
(c) 6 R
(d) 36 R

Answer: C

Question. A particle moves in a circle of radius 4 cm clockwise at constant speed 2 cm/s. If ˆx and ˆy are unit acceleration vectors along X and Y-axis respectively (in cm/s²), the acceleration of the particle at the instant half way between P and Q is given by 

Answer: C

Question. From a point on the ground at a distance 2 meters from the foot of a vertical wall, a ball is thrown at an angle of 45º which just clears the top of the wall and afterward strikes the ground at a distance 4 m on the other side. The height of the wall is
(a) 2/3 m
(b) 3/4 m
(c) 1/3 m
(d) 4/3 m

Answer: D

Question. Given that A + B = R and A = B = R. What should be the angle between A and B ?
(a) 0
(b) π/3
(c) 2π/3
(d) π

Answer: C

Question. Out of the following sets of forces, the resultant of which cannot be zero ?
(a) 10, 10, 10
(b) 10, 10, 20
(c) 10, 20, 20
(d) 10, 20, 40

Answer: D

Question. A rectangular sheet of material has a width of 3 m and a length of 4 m. Forces with magnitudes of 3 N and 4N.
respectively, are applied parallel to two edges of the sheet, as shown in the figure below. 

A third force F, is applied to the centre of the sheet, along a line in the plane of the sheet, at an angle q = tan 0.75 with respect to the horizontal direction. The sheet will be in translational equilibrium when F has what value?
(a) F = 3 N
(b) F = 4N
(c) F = 5 N
(d) F = 7N

Answer: C

Question. Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are
(a) 12 N, 6 N
(b) 13 N, 5 N
(c) 10 N, 8 N
(d) 16N, 2N

Answer: B

Question. For any two vectors A̅ and B̅ , if A̅.B̅ = |A̅ x B̅|, the magnitude of C̅ = A̅ + B̅ is 
(a) A + B 
(b) √A² + B² + √2 AB
(c) √A² + B²
(d) √A² + B² + AB/√2

Answer: B

Question. Let A = iA cos q + jA sin q be any vector. Another vector B, which is normal to A can be expressed as
(a) i B cos θ – j B sin θ
(b) i B cos θ + j B sin θ
(c) i B sin θ – j B cos θ
(d) i B sin θ + j B cos θ

Answer: C

Question. Let C̅ = A̅ + B̅
(a) |C̅|is always greater than |A̅|
(b) It is possible to have |C̅|<|A̅|and |C̅|<|B̅|
(c) C̅ is always equal to A̅ + B̅
(d) C̅ is never equal to A̅ + B̅

Answer: B

Question. The velocity of projection of a body is increased by 2%. Other factors remaining unchanged, what will be the percentage change in the maximum height attained?
(a) 1%
(b) 2 %
(c) 4 %
(d) 8 %

Answer: C

Question. A ball is thrown from the ground with a velocity of 20 √3 m/s making an angle of 60º with the horizontal. The ball will be at a height of 40 m from the ground after a time t equal to (g = 10 ms^–2)
(a) √2 sec
(b) √3 sec
(c) 2 sec
(d) 3 sec

Answer: C

Question.  A moves with 65 km/h while B is coming back of A with 80 km/h. The relative velocity of B with respect to A is
(a) 80 km/h
(b) 60 km/
(c) 15 km/h
(d) 145 km/h

Answer: C

Question. How many minimum number of vectors in different planes can be added to give zero resultant?
(a) 2
(b) 3
(c) 4
(d) 5

Answer: C

Question. Angular momentum is
(a) a scalar
(b) a polar vector
(c) an axial vector
(d) None of these

Answer: C

Question. The component of a vector r along x-axis will have maximum value if
(a) r is along positive y-axis
(b) r is along positive x-axis
(c) r makes an angle of 45° with the x-axis
(d) r is along negative y-axis

Answer: B

Question. Which of the following is an essential condition for horizontal component of projectile to remain constant?
(a) Acceleration due to gravity should be exactly constant
(b) Angle of projection should be 45°
(c) There should be no air-resistance
(d) All of these

Answer: C

Question.  The shape of trajectory of the motion of an object is determined by
(a) acceleration
(b) initial position
(c) initial velocity
(d) All of these

Answer: D

Question. In the projectile motion, if air resistance is ignored, the horizontal motion is at
(a) constant acceleration
(b) constant velocity
(b) variable acceleration
(d) constant retardation

Answer: B

Question. A scalar quantity is one that
(a) can never take negative values
(b) has magnitude as well as direction
(c) does not vary from one point to another in space
(d) has the same value for observers with different orientations of axes.

Answer: D

Question. A bullet is dropped from the same height when another bullet is fired horizontally. They will hit the ground
(a) one after the other
(b) simultaneously
(c) depends on the observer
(d) None of these

Answer: B 

Question.  It is found that | A + B | = | A |. This necessarily implies,
(a) B = 0
(b) A and B are antiparallel
(c) A and B are perpendicular
(d) A.B < 0

Answer: B

Question. Consider the quantities pressure, power, energy, impulse, gravitational potential, electric charge, temperature and area. Out of these, the vector quantities are
(a) impulse, pressure and area
(b) impulse and area
(c) area and gravitational potential
(d) impulse and pressure

Answer: B

Question. The time of flighAt of a projectile on an upward inclined plane depends upon
(a) angle of inclination of the plane
(b) angle of projection
(c) the value of acceleration due to gravity
(d) all of the above.

Answer: D

Question. Which of the following conditions are sufficient and essential for a quantity to be a vector?
(a) Magnitude and direction
(b) Magnitude and addition, subtraction, multiplication by ordinary rules of algebra
(c) Magnitude, direction, and addition, subtraction multiplication and division by vector laws
(d) Magnitude, direction and combination of vectors by ordinary rules of algebra

Answer: C

Question. At the highest point on the trajectory of a projectile, its
(a) potential energy is minimum
(b) kinetic energy is maximum
(c) total energy is maximum
(d) kinetic energy is minimum.

Answer: D

Question. If ar and at represent radial and tangential accelerations, the motion of particle will be uniformly circular, if
(a) ar = 0 and at = 0
(b) ar = 0 but at ≠ 0
(c) ar ≠ 0 and at = 0
(d) ar ≠ 0 and at ≠ 0

Answer: C

Question. The angular speed of a fly-wheel making 120 revolutions/ minute is
(a) π rad/sec
(b) 4π rad/sec
(c) 2π rad/sec
(d) 4π² rad/sec

Answer: B

Question. Consider two vectors F̅₁ = 2î + 5k̂and F̅₂ = 3ĵ + 4k̂.The magnitude of the scalar product of these vectors is
(a) 20
(b) 23
(c) 5 √33
(d) 26

Answer: A

Question. A bomb is dropped from an aeroplane moving horizontally at constant speed. If air resistance is taken into consideration, then the bomb
(a) falls on earth exactly below the aeroplane
(b) falls on the earth exactly behind the aeroplane
(c) falls on the earths ahead of the aeroplane
(d) flies with the aeroplane

Answer: B

Question. If A and B are two vectors, then the correct statement is
(a) A + B = B + A
(b) A – B = B – A
(c) A × B = B × A
(d) None of these

Answer: A

Question. A projectile is thrown in the upward direction making an angle of 60° with the horizontal direction with a velocity of 147 ms–1. Then the time after which its inclination with the horizontal is 45°, is
(a) 15 s
(b) 10.98 s
(c) 5.49 s
(d) 2.745 s

Answer: C

Question. A projectile of mass m is fired with velocity u making angle θ with the horizontal. Its angular momentum about the point of projection when it hits the ground is given by
(a) 2musin²θcosθ/g
(b) 2mu³ sin²θcosθ/g
(c) musin²θcosθ/2g
(d) mu³sin²θcosθ/2g

Answer: B

Question. If A = B + C and the magnitudes of A, B and C are 5, 4 and 3 units, the angle between A and C is
(a) cos^–1 (3/5)
(b) cos^–1 (4/5)
(c) π/2
(d) sin^–1 (3/4)

Answer: A

Question. The greatest height to which a man can through a ball is h.
What is the greatest horizontal distance to which he can throw the ball?
(a) 2h
(b) h/4
(c) h/2
(d) None of these

Answer: A

Question. A cannon on a level plane is aimed at an angle θ above the horizontal and a shell is fired with a muzzle velocity v₀ towards a vertical cliff a distance D away. Then the height from the bottom at which the shell strikes the side walls of the cliff is 

Answer: C

Question. If range is double the maximum height of a projectile, then q is
(a) tan^–14
(b) tan^–1 1/4
(c) tan^–1 1
(d) tan–1 2

Answer: D

Question. In uniform circular motion, the velocity vector and acceleration vector are
(a) perpendicular to each other
(b) same direction
(c) opposite direction
(d) not related to each other

Answer: A

Question. Two vectors A and B lie in a plane, another vector C lies outside this plane, then the resultant of these three vectors i.e., A + B + C
(a) can be zero
(b) cannot be zero
(c) lies in the plane containing A + B
(d) lies in the plane containing A – B

Answer: B

Question. A body is projected such that its KE at the top is 3/4th of its initial KE. What is the angle of projectile with the horizontal?
(a) 30º
(b) 60º
(c) 45º
(d) 120º

Answer: A

Question. A projectile can have the same range for two angles of projection. If h₁ and h₂ are maximum heights when the range in the two cases is R, then the relation between R, h₁ and h₂ is
(a) R =4√h₁h₂
(b) R = 2√h₁h₂
(c) R = √h₁h₂
(d) None of these

Answer: A

Question. Consider a vector F = 4 i – 3 j. Another vector that is perpendicular to F is
(a) 4 i + 3 j
(b) 6 i
(c) 7 k
(d) 3 i – 4 j

Answer: C

Question. Forces of 4 N and 5 N are applied at origin along X-axis and Y-axis respectively. The resultant force will be
(a) √41N,tan^-1(5/4)
(b) √41N,tan^-1(4/5)
(c) -√41N,tan^-1(5/4)
(d) -√41N,tan^-1(4/5)

Answer: A

Question. A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in meter per second² is
(a) π²
(b) 8 π²
(c) 4 π²
(d) 2 π²

Answer: C

Question. The vector sum of the forces of 10 N and 6 N can be
(a) 2 N
(b) 8 N
(c) 18 N
(d) 20 N

Answer: B

Question. Given that A + B = R and A² + B² = R². The angle between A and B is
(a) 0
(b) π/4
(c) π/2
(d) π

Answer: C

Question. A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of 60 km h^–1 and at a height of 490 m. At the time of dropping the bomb, how far the aeroplane should be from the enemy post so that the bomb may directly hit the target ?
(a) 400/3 m
(b) 500/3 m
(c) 1700/3 m
(d) 498 m.

Answer: B

Question. The force required to keep a body in uniform circular motion is
(a) centripetal force
(b) centrifugal force
(c) resistance
(d) None of these

Answer: A

Question. The vertical component of velocity of a projectile at its maximum height (u - velocity of projection, θ-angle of projection) is
(a) u sinθ
(b) u cos θ
(c) u / sin θ
(d) 0

Answer: D

Question. At the top of the trajectory of a projectile, the acceleration is
(a) maximum
(b) minimum
(c) zero
(d) g

Answer: D

Question. Centripetal acceleration is
(a) a constant vector
(b) a constant scalar
(c) a magnitude changing vector
(d) not a constant vector

Answer: D

Question. For projectile motion, we will assume that the air resistance has ...X... effect on the motion of the projectile. Here, X refers to
(a) sufficient
(b) insufficient
(c) negligible
(d) proper

Answer: C

Question. In a vertical circle of radius r at what point in the path a particle has tension equal to zero if it is just able to complete the vertical circle?
(a) Highest point
(b) Lowest point
(c) Any point
(d) At a point horizontally from the centre of circle of radius r

Answer: A

Question. For an object thrown at 45° to horizontal, the maximum height (H) and horizontal range (R) are related as
(a) R = 16 H
(b) R = 8 H
(c) R = 4 H
(d) R = 2H

Answer: C

Question. Two stones are moving with same angular speeds in the radii of circular paths 1 m and 2 m. The ratio of their linear speed is ...X.... Here, X refers to
(a) 2
(b) 1/2
(c) 1/3
(d) 3

Answer: B

Question. The direction of the angular velocity vector is along
(a) the tangent to the circular path
(b) the inward radius
(c) the outward radius
(d) the axis of rotation

Answer: D

Question. The angle of projection, for which the horizontal range and the maximum height of a projectile are equal, is:
(a) 45°
(b) θ = tan^–14
(c) θ = tan^–1 (0.25)
(d) none of these.

Answer: B

Question. In uniform circular motion
(a) both velocity and acceleration are constant
(b) acceleration and speed are constant but velocity changes
(c) both acceleration and velocity change
(d) both acceleration and speed are constant

Answer: C

Question. If a particle moves in a circle describing equal angles in equal interval of time, its velocity vector
(a) remains constant
(b) changes in magnitude
(c) changes in direction
(d) changes both in magnitude and direction

Answer: C

Question. When a body moves with a constant speed along a circle
(a) no work is done on it
(b) no acceleration is produced in the body
(c) no force acts on the body
(d) its velocity remains constant

Answer: A

Question. A body is moving with a constant speed v in a circle of radius r. Its angular acceleration is
(a) vr
(b) v/r
(c) zero
(d) vr²

Answer: C

Question. Which of the following is not correct ?
(a) A̅ x B̅ = -B̅ x A̅
(b) A̅ x B̅ ≠ B̅ x A̅
(c) A̅ x (B̅ +C̅) = A̅ x B̅ + A̅ x C̅
(d) A̅ x (B̅ + C̅) = ( A̅ x B̅) + C̅

Answer: D

Question. The magnitude of the vector product of two vectors is √3 times the scalar product. The angle between vectors is
(a) π/4
(b) π/6
(c) π/ 3
(d) π/2

Answer: C

Question. If ˆn is a unit vector in the direction of the vector A, then 

Answer: A

Question. The time of flight of a projectile on an upward inclined plane depends upon
(a) angle of inclination of the plane
(b) angle of projection
(c) the value of acceleration due to gravity
(d) all of the above.

Answer: D

Question. Three particles A, B and C are projected from the same point with same initial speeds making angles 30º, 45º and 60º respectively with the horizontal. Which of the following statements is correct?
(a) A, B and C have unequal ranges
(b) Ranges of A and C are equal and less than that of B
(c) Ranges of A and C are equal and greater than that of B
(d) A, B and C have equal ranges

Answer: C

Question. Three vectors A, B and C satisfy the relation A · B = 0 and A · C = 0. The vector A is parallel to
(a) B
(b) C
(c) B · C
(d) B × C

Answer: D

Question. At what angle must the two forces (x + y) and (x – y) act so that the resultant may be √(x² + y²) ?

Answer: A

Question. Two particles of equal masses are revolving in circular paths of radii r₁ and r₂ respectively with the same period. The ratio of their centripetal force is
(a) r₁/r2
(b) √r₂ / r₁
(c) (r₁/r₂)²
(d) (r₂/r₁)²

Answer: A

Question. A bomb is released from a horizontal flying aeroplane. The trajectory of bomb is
(a) a parabola
(b) a straight line
(c) a circle
(d) a hyperbola

Answer: A

Question. It is found that A+ B = A . This necessarily implies,
(a) B = 0
(b) A, B are antiparallel
(c) A, B are perpendicular
(d) A.B ≤ 0

Answer: B

Question. Which one of the following statements is true?
(a) A scalar quantity is the one that is conserved in a process.
(b) A scalar quantity is the one that can never take negative values.
(c) A scalar quantity is the one that does not vary from one point to another in space.
(d) A scalar quantity has the same value for observers with different orientations of the axes.

Answer: D

Question. Two balls are projected at an angle q and (90º – θ) to the horizontal with the same speed. The ratio of their maximum vertical heights is
(a) 1 : 1
(b) tanv : 1
(c) 1 : tanv
(d) tan²θ : 1

Answer: D

Question. A force of k̂ – F acts on O, the origin of the coordinate system. The torque about the point (1, –1) is 

(a) F(î - ĵ)
(b) -F(î + ĵ)
(c) F(î + ĵ)
(d) -F(î - ĵ)

Answer: C

Question. A projectile thrown with velocity v making angle θ with vertical gains maximum height H in the time for which the projectile remains in air, the time period is
(a) √Hcos θ/g
(b) √2Hcos θ/g
(c) √4H/g
(d) √8H /g

Answer: D

Question. Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown up, B is thrown down and C is horizontally. They hit the ground with speeds v_A, v_B and v_C respectively then,
(a) v_A = v_B = v_C
(b) v_A = v_B > v_C
(c) v_B > v_C > v_A
(d) vA > v_B = v_C

Answer: A

Question. An aeroplane flying at a constant speed releases a bomb.
As the bomb moves away from the aeroplane, it will
(a) always be vertically below the aeroplane only if the aeroplane was flying horizontally
(b) always be vertically below the aeroplane only if the aeroplane was flying at an angle of 45° to the horizontal
(c) always be vertically below the aeroplane
(d) gradually fall behind the aeroplane if the aeroplane was flying horizontally.

Answer: C

Question. At the highest point on the trajectory of a projectile, its
(a) potential energy is minimum
(b) kinetic energy is maximum
(c) total energy is maximum
(d) kinetic energy is minimum.

Answer: D

Question. A projectile is projected with a kinetic energy E. Its range is R.
It will have the minimum kinetic energy, after covering a horizontal distance equal to
(a) 0.25 R
(b) 0.5 R
(c) 0.75 R
(d) R

Answer: B

Question. The range of a projectile when launched at an angle of 15º with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of 45º to the horizontal
(a) 1.5 km
(b) 3.0 km
(c) 6.3 km
(d) 0.75 km

Answer: B

Question. A gun fires two bullets at 60º and 30º with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio
(a) 2 : 1
(b) 3 : 1
(c) 4 : 1
(d) 1 : 1

Answer: B

Question. A stone is just released from the window of a moving train moving along a horizontal straight track. The stone will hit the ground following a
(a) straight line path
(b) circular path
(c) parabolic path
(d) hyperbolic path

Answer: C

Question. A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v, if the string is released the stone flies
(a) radially outward
(b) radially inward
(c) tangentially outward
(d) with an acceleration mv2/l

Answer: C

Question. A particle moves in a plane with a constant acceleration in a direction different from the initial velocity. The path of the particle is a/an
(a) straight line
(b) arc of a circle
(c) parabola
(d) ellipse

Answer: C

Question. In uniform circular motion, the velocity vector and acceleration vector are
(a) perpendicular to each other
(b) same direction
(c) opposite direction
(d) not related to each other

Answer: A

Question. A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant
(a) acceleration
(b) velocity
(c) momentum
(d) kinetic energy

Answer: D

Question. The coordinates of a particle moving in x–y plane at any instant of time t are x = 4t2; y = 3t2. The speed of the particle at that instant is
(a) 10 t
(b) 5 t
(c) 3 t
(d) 2 t

Answer: A

Question. For motion in two or three dimensions, the angle between velocity and acceleration is
(a) 0°
(b) 90°
(c) 180°
(d) Any angle between 0° & 180°

Answer: D

Question. The circular motion of a particle with constant speed is
(a) periodic but not simple harmonic
(b) simple harmonic but not periodic
(c) periodic and simple harmonic
(d) neither periodic nor simple harmonic

Answer: A

Question. Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first?
(a) Slower one
(b) Faster one
(c) Both will reach simultaneously
(d) It cannot be predicted

Answer: C

Question. A body is travelling in a circle at a constant speed. It
(a) has a constant velocity
(b) is not accelerated
(c) has an inward radial acceleration
(d) has an outward radial acceleration

Answer: C