NCERT Exemplar Solutions Class 9 Science Work and Energy

Multiple Choice Questions (MCQs).............................

Question 1: When a body falls freely towards the earth, then its total energy
(a) increases
(b) decreases
(c) remains constant
(d) first increases and then decreases

Solution 1:   (c) remains constant. 

Since a system's total energy is always conserved, as a body falls freely into the planet, its total energy stays unchanged, i.e., the amount of the body's potential and kinetic energy is the same at all times.

Question 2: A car is accelerated on a leveled road and attains a velocity 4 times of its initial velocity. In this process,
the potential energy of the car
(a) does not change
(b) becomes twice to that of initial
(c) becomes 4 times that of initial
(d) becomes 16 times that of initial

Solution 2:  (a) does not change. 

The car's potential energy does not change, but its kinetic energy does changes by as follows
Let, initial velocity = u

                                           Kinetic energy K₁ = ½ mu²                                                                                         … (i)

Given, after sometime velocity becomes 4 times of its initial velocity

i.e., final velocity (v) = 4u 

Now, put v = 4u, in Eq. (i), we get

                                                     Kinetic energy = ½ m (4u) ²

                                                                         = ½ m 16u²     

                                                                     K₂ = 16 ½ mu²    

From Eq. (i),                                                 K₂ = 16 K₁
As a result of this process, the car's kinetic energy increases to 16 times its initial value.

Question 3: In case of negative work, the angle between the force and displacement is

(a) 0                    

(b) 45°                       

(c) 90°                       

(d) 180°

Solution 3:   (d) 180°.  

(a) Work done W = F .d cos 0
      ∴Work done at θ= 0°, W = F .d cos 0°                                                                                          (∴ cos 0° = 1)
       =>                                 W = F .d
       For angle θ = 0°,

 Work done Is positive, so it is not true.
(b) We know that work done, W = F .d cos 0
                                             W = F .d cos 45°                                                                                

                                             W =
       For angle 0 = 45°,
      work done is positive, so it is not true.
(c) We know that work done, W = d cos θ
     Work done at θ = 90°,        W = F .d cos 90°                                                                                 (∴ cos 90° = 0)
                                           W = 0
     So, it is not true.
(d) Work done at θ = 180°, W = F .d cos θ                                                                                      (∴ cos 180°= -1)
                                          W = -F. d
The angle between the force and the displacement should be 180° for negative work. (i.e., force and displacement are diametrically opposed) So, yes, it is right.

Question 4: An iron sphere of mass 10 kg has the same diameter as an aluminium sphere of mass 3.5 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same

(a) acceleration                                         

(b) momenta

(c) potential energy                                  

(d) kinetic energy

Solution 4:  (a) acceleration. 

When two spheres are dropped from a tower at the same time, they have the same acceleration. That during free fall, the body's acceleration equals (g = 9.8 m/s2), and "g" is determined by the mass and radius of the earth

Question 5: A girl is carrying a school bag of 3 kg mass on her back and moves 200 m on a leveled road. The work done against the gravitational force will be (9 = 10 ms⁻²)

(a) 6 x 10³ J                                  

(b) 6 J                       

(c) 0.6 J                    

(d) zero

Solution 5:   (d) zero.

We know that, work done = F .d cos 0
Force on school bag makes an angle 90° from the road.

i.e.,                                            0 = 90°
                                                    W = F .d cos 90°                                                                                (∴ cos 90° = 0°)
                                                    W = 0
The work performed against the gravitational force is zero, according to Flense.

Question 6: Which one of the following is not the unit of energy?

(a) Joule                  

(b) Newton metre                           

(c) Kilowatt                   

(d) Kilowatt hour

Solution 6:   (c) Kilowatt.

The units of energy are the joule, newton metre, and kilowatt hour, and the unit of power is the kilowatt.

Question 7: The work done on an object does not depend upon the
(a) displacement
(b) force applied
(c) angle between force and displacement
(d) initial velocity of the object

Solution 7:   (d) initial velocity of the object.

We know that, W = F .d cos 0
Here, F denotes the force applied to the object, d denotes the displacement and 0 denotes the angle formed by the force and displacement. As a result, the work done on an object is independent of its initial velocity.

Question 8: Water stored in a dam possesses

(a) no energy                                            

(b) electrical energy

(c) kinetic energy                                      

(d) potential energy

Solution 8:   (d) potential energy.

Water stored in a dam has potential energy since it is stored energy or the energy of position.

Question 9:  A body is falling from a height h. After it has fallen a height it will possess
(a) only potential energy
(b) only kinetic energy
(c) half potential and half kinetic energy
(d) more kinetic and less potential energy

Solution 9:  (c) half potential and half kinetic energy.

As we know that when a body is at height h, it has total energy = KE + PE

And at height ‘h’, velocity of body is zero.

So,                               KE = 0 and PE = mgh

So,               total energy = mgh + 0 = mgh

Short Answer Type Questions......................

Question 10:  A rocket is moving up with a velocity v. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies?

Solution 10:

Given, v₁ = v and v₂ = 3v

  Kinetic energy of rocket (K) = ½ mv²

Question 11:  Avinash can run with a speed of 8 ms^-1 against the frictional force of 10 N and Kapil can move with a speed of 3 ms^-1 against the frictional force of 25 N. Who is more powerful and why?

Solution 11:
Given, force applied by Avinash = 10 N
Speed of Avinash = 8 ms^-1                                               ‘
Power of Avinash = F.v = 10×8 = 80W
Now, force applied by Kapil = 25 N
Speed of Kapil = 3ms^-1
Power of Kapil = F.v = 25×3 = 75W
Since Avinash has more power than Kapil i.e. (80 – 75) = 5 W. As a result, Avinash is the stronger of the two.

Question 12:  A boy is moving on a straight road against a frictional force of 5 N. After travelling a distance of 1.5 km, he forgot the correct path at a roundabout of radius 100 m as shown in figure. However, he moves on the circular path for one and half cycle and then he moves forward up to 2.0 km. calculate the work done by him.

Solution 12:
Given, force applied by boy against friction = 5 N
Displacement on the circular path = One cycle + Half cycled = 0 + Half cycle
                                                      = 0 + Diameter of circular path 

                                                            (∴ Displacement depends on initial and final point)

                                                     = 0+ 2r

                                                    = 0+2×100                                                                                                [∴r = 100m]
                                                    = 0 + 200 = 200 m
∴ Total displacements = 1.5 km + 200 m + 2.0 km
                                    = 1.5 x 1000 + 200 + 2 x 1000km                                                              (1 km= 1000 m)
                                    = 3700 m
Work done by boy = F .s cos θ
                              = 5 x 3700 x cos 0

                              = 18500 J

Question 13: Can any object have mechanical energy even if its momentum is zero?

Solution 13:

Mechanical energy is equal to the sum of kinetic and potential energy.

And since the body's momentum is zero, its velocity is also zero, implying that its kinetic energy is also zero. However, it may be a source of energy in the future.

Even if a body's momentum is zero, it can still have mechanical energy.

Question 14:  Can any object have momentum even if its mechanical energy is zero? Explain.

Solution 14:

Since, mechanical energy = potential energy + kinetic energy

If mechanical energy = 0

So,      PE + KE= 0

⇒           PE = -KE
Since mechanical energy is equal to the sum of potential and kinetic energy,

So, if mechanical energy is zero, we can assume that a body has momentum.

Question 15:  The power of a motor pump is 2 kW. How much water per minute, the pump can raise to a height of 10 m?                                                                          [given, g = 10 ms^-2]

Solution 15:

Given, power of a motor = 2kW = 2× 1000 W = 2000W                                                        [ 1kW = 1000 W]

Question 16:  The weight of a person on a planet A is about half that on the earth. He can jump up to 0.4 m height on the surface of the earth. How high he can jump on the planet A?  

Solution 16:

It is given that weight of person on the earth = w                                                                             (i.e., w = mg)

And as he can jump up to height (h, = 0.4m)

So, potential energy at this point = mgh = mg x 0.4                                                                                          …(i)