Question

What should be the change in velocity of a body, if its mass is increased by four times for the same K.E of the body?

Answer 1

Let,

1. Initial velocity = $u$ and initial mass = $m$
2. Final velocity = $v$ and final mass = $4\times m$

K.E remains same.

$K.E_{initial}=K.E_{final}$

$\frac{1}{2}m{u}^2=\frac{1}{2}(4\times m)v^2$

$u^2=4\times v^2$

$v^2=\frac{u^2}{4}$

$v=\frac{u}{2}$

$\therefore$ The velocity of a body should be halved, if its mass is increased by four times for the same K.E. of the body.