Question

If the linear momentum of a sphere is doubled, its kinetic energy will become _________ its original value.

• A. twice
• B. four times
• C. eight times
• D. sixteen times

Answer 1

The correct option is B four times

KE$=\frac{1}{2}\frac{p^2}{m}$

If $p_2=2p$

$K.E_2=\frac{1}{2}\frac{{{(\overrightarrow{p}}_2)}^2}{m}=\frac{1}{2}\times \frac{(2p{)}^2}{m}$

$=4\left(\frac{1}{2}\frac{p^2}{m}\right)=4K.E$