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Question: A body of mass 4 kg is moving with momentum of \(8 \mathrm {~kg} \mathrm {~ms} ^ { - 1 }\). A force ...

A body of mass 4 kg is moving with momentum of 8 kg ms−18 \mathrm {~kg} \mathrm {~ms} ^ { - 1 }. A force of 0.2 N acts on it in the direction of motion of the body for 10 s. The increase in kinetic energy is

A

10 J

B

8.5 J

C

4.5 J

D

4 J1

Answer

4.5 J

Explanation

Solution

Momentum = mass × velocity

p=mu\mathrm { p } = \mathrm { mu }

u=pm=8 kg m−14 kg=\mathrm { u } = \frac { \mathrm { p } } { \mathrm { m } } = \frac { 8 \mathrm {~kg} \mathrm {~m} ^ { - 1 } } { 4 \mathrm {~kg} } = 2 ms−12 \mathrm {~ms} ^ { - 1 }

Acceleration = Force  Mass = \frac { \text { Force } } { \text { Mass } }

a=0.2 N4 kg=0.05 m s−1\mathrm { a } = \frac { 0.2 \mathrm {~N} } { 4 \mathrm {~kg} } = 0.05 \mathrm {~m} \mathrm {~s} ^ { - 1 }

Distance travelled by the body in 10 s is

d=ut+12at2\mathrm { d } = \mathrm { ut } + \frac { 1 } { 2 } \mathrm { at } ^ { 2 }

=(2 ms−1)(10 s)+12×(0.05 ms−2)(10 s)2= \left( 2 \mathrm {~ms} ^ { - 1 } \right) ( 10 \mathrm {~s} ) + \frac { 1 } { 2 } \times \left( 0.05 \mathrm {~ms} ^ { - 2 } \right) ( 10 \mathrm {~s} ) ^ { 2 }

=20 m+2.5 m=22.5 m= 20 \mathrm {~m} + 2.5 \mathrm {~m} = 22.5 \mathrm {~m}

Work done, W= fd = (0.2N) (22.5m) = 4.5 J

According to work-energy theorem

Increase in kinetic energy = work done = 4.5 J