Question

If momentum is increased by 20%, then kinetic energy increases by

• A. 48%
• B. 44%
• C. 40%
• D. 36%

Answer 1

Answer: (B)

The kinetic energy is given by KE = $\frac{p^2}{2m}$
So, $△KE=\frac{2p△p}{2m}=\frac{p△p}{m}$
$\Rightarrow \frac{4KE}{KE}=\frac{2△p}{p}$
Thus, the final momentum becomes 1.2 p
So, percentage change in KE = $\frac{finalKE-initialKE}{initialKE}\times 100$
= $\frac{1.44(p^2/2m)-(p^2/2m)}{(p^2/2m)}$ = 44%