Question

Assertion :In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun. Reason: Kinetic energy $\propto \frac{1}{mass}$; if momentum is constant.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

From conservation of momentum,
$p_{bullet}=p_{gun}$

$K=\frac{p^2}{2m}$;

$\Rightarrow K\propto \frac{1}{m};$

$\Rightarrow \sqrt{2K_{bullet}{m}_{bullet}}=\sqrt{2K_{gun}{m}_{gun}}$;

$\Rightarrow \frac{K_{bullet}}{K_{gun}}=\frac{m_{gun}}{m_{bullet}}$;

$\Rightarrow K\alpha \frac{1}{m}$