Question

When linear momentum of a body becomes n times, its kinetic energy becomes ______.

Options

• n² times

• `1/(n^2)` times

• n³ times

• `1/(n^3)` times

Answer 1

When linear momentum of a body becomes n times, its kinetic energy becomes n² times.

Explanation:

For a body of constant mass,

K = `p^2/(2 m)`

Thus, kinetic energy is proportional to the square of momentum:

K ∝ p²

If the momentum becomes n times,

p' = np

then, 

K' ∝ (np)²

= n²p²

Therefore, the kinetic energy becomes n² times.