Question

when the speed of a particle is doubled the ratio of its kinetic energy to its Momentum will be

Answer 1

if we double the speed , the ratio will be doubled.

Answer 2

New ratio is 4:2 or 2:1

Explanation:

The kinetic energy of the particle is given by :

$k=\dfrac{1}{2}mv^2$

The momentum of the particle is given by :

p = mv

When the speed of a particle is doubled, v' = 2v

New kinetic energy is given by :

$k'=\dfrac{1}{2}mv'^2$  

$k'=\dfrac{1}{2}m(2v)^2$.................(1)

New momentum is given by :

p' = mv'

$p'=m(2v)$.............(2)

It is clear that,

k' = 4 k

And

p' = 2 p

So, the ratio of new kinetic energy to its Momentum will be be 4:2 or 2:1. Hence, this is the required solution.

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Topic : Momentum and kinetic energy

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