Question

If kinetic energy of a body becomes four times, then its new momentum will:

• A. become four times its initial value
• B. become two times its initial value
• C. become half of its initial value
• D. remain constant

Answer 1

Answer: (B)

The relation between kinetic energy $K$,
and momentum $p$ is $ p=\sqrt{2\,mK} $
where m is mass of the body.
Given, $ {{K}_{1}}=K,\,\,{{K}_{2}}=4\,K $ ,
$ \therefore \frac{{{p}_{1}}}{{{p}_{2}}}=\frac{\sqrt{2\,mK}}{\sqrt{2\,m\,(4K)}}=\frac{1}{2} $
$ \Rightarrow {{p}_{2}}=2\,{{p}_{1}} $
Hence, momentum becomes two times of its initial value.