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Question

If the kinetic energy of a body is increased two times, its momentum will


A

Half

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B

Remain unchanged

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C

Be doubled

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D

Increases 2 times

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Solution

The correct option is D

Increases 2 times


Step 1: Given data

The kinetic energy of a body is increased two times,

K'=2K

K = kinetic energy

K'= new Kinetic Energy

Step 2: Formula used

Momentum (ρ) can be written as,
ρ=mv

v is the velocity of the body

m is the mass of the body

The kinetic energy in terms of momentum is K=12mv2

The relation between kinetic energy and momentum (ρ) is
K=ρ22m

or ρ=2mK

Step 3: Evaluate the new momentum

ρ'=2mK'

ρ'=2m(2K)

ρ'=2ρ

ρ is the momentum of the body, and ρ' is the new momentum when kinetic energy is doubled.

So If the kinetic energy of a body is increased two times, its momentum will be 2 times the momentum.

Hence, option D is the correct answer.


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