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Class IX – Work & Energy

Important Questions

1. A force of 18 N is acting on an object. The object is displaced through 3 m in the direction of force. What is the work done?

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Ans. F = 18 N

S = 3 m

Work done = F x S

            = 18 x 3

            = 54 J

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2. If a particle of mass 5 kg moves uniformly along a circle of radius 10 m at 10 m/s, then what is the work done by centripetal force during its one revolution?

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Ans. Work done = 0

 Since displacement = 0

3. The work done against gravity in taking 10 kg mass at 1m height in 1 sec will be?

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Ans. m = 10 kg

h = 1 m

g = 9.8 m/s2

Work done = m x g x h

            = 10 x 9.8 x 1

            = 98 J

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4. A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage (g = 10 m/s2)

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Ans. m = 15 kg

h = 1.5 m

g = 10 m/s2

Work done = m x g x h

            = 15 x 10 x 1.5

            = 225 J

5. A girl is carrying a school bag of 3 kg mass on her back and moves 200 m on a levelled road. The work done against the gravitational force will be (g= 10m/s2)

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Ans.

If θ = 0 => Work done = F x S cos 0 = F x S

If θ = 90 => Work done = F x S cos 90 = 0

In this case θ = 90

Work done = 0

6. An object of mass 15 kg is moving with a uniform velocity of 4 m/s. What is the kinetic energy possessed by the object?

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m = 15 kg

v = 4 m/s

K.E = ½ mv2

            = ½ x 15 x 4 x 4

            = 120 J

7. The kinetic energy of an object of mass, m moving with velocity of 5 m s -2 is 25 J. What will be its kinetic energy when its velocity is doubled?

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Ans. K.E = 25 J

v = 5 m/s

K.E = ½ mv2

            = ½ x m x 52 = 25

m = 2 kg

K.E = ½ x 2 x 10 x 10

            = 100 J

If velocity becomes double, K.E becomes four times

K.E = 4 x 25

            = 100 J

8. The kinetic energy of an object of mass m moving with a velocity of 5 m s-2 is 25 J. What will be its kinetic energy when its velocity is tripled?

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Ans. K.E = 25 J

v = 5 m/s

K.E = ½ mv2

            = ½ x m x 52 = 25

m = 2 kg

K.E = ½ x 2 x (15)2

            = 225 J

If velocity is tripled, K.E becomes 9 times

K.E = 9 x 25 = 225 J

9. Find the energy possessed by an object of mass 10 kg when its is at a height of 6 m above the ground. Given g = 9.8 m s -2

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m = 10 kg

h = 6 m

g = 9.8 m/s2

P.E = m x g x h

            = 10 x 9.8 x 6

            = 588 J

10. An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground, Given g = 10m/s2

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Ans. m = 12 kg

P.E = 480 J

h = ?

g = 10 m/s2

P.E = m x g x h

480 = 12 x 10 x h

h = 480/120

= 4 m

11. Find the work done by a force of 5 N in displacing a book through 20 cm along the direction of the push.

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Ans. F = 5 N

s = 20 cm = 20/100 = 0.2 m

Work done = F x s

            = 5 x 0.2

            = 1 J

12. When the mass and velocity of the body are doubled, what happens to its kinetic energy?

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Ans. K.E = ½ mv2

K.E’ = ½ x (2m) x (2v)2

K.E’ = ½ x 2m x 4v2

K.E’ = ½ mv2 x 8

K.E’ = K.E x 8

13.  A block of wood of mass 250 g is moving at a speed of 4 ms-1. Find its K.E in Joules

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Ans. m = 250 g = 250/1000 = ¼ kg

v = 4 m/s

K.E = ½ x m x v2

            = ½ x ¼ x 4 x 4

K.E = 2J

14. A girl of mass 40 kg climbs 50 stairs each of average height 20 cm. Find the potential energy of the girl on reaching the top. (g = 10ms-2)

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Ans. m = 40 kg

g = 10 m/s2

h = 50 x 20/100 = 10 m

P.E = m x g x h

            = 40 x 10 x 10

            = 4000 J

15. A body is falling from a height h. After it has fallen from a height h/2, it will possess ________

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Ans. h = h/2

P.E = mgh/2 = K.E

P.E will become half of its initial value is equal to K.E

16. 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?

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K.E = ½ mv2

K.E’ = ½ m (3v)2

            = 9 x ½ mv2

K.E/K.E’ = 1/2mv2/9 x 1/2mv2 = 1/9

1 : 9

17. A force of 100 N works on a body in the direction of motion of body while body completes a revolution on a square path of side 1 m. Total work done is :

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Ans. Since displacement = 0

F = 100 N

Work done = F x S

            = 100 x 0

            = 0 J

18. What is the velocity of a body of mass 100 g having K.E of 20 J?

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Ans. m = 100 g = 100/1000 kg = 0.1 kg

K.E = 20 J

K.E = ½ mv2

20 = ½ x 0.1 x v2

v2 = 400

v = 20 m/s