Question

Assertion :A gun of mass $M$ fires a bullet of mass $m$, the ratio of recoil energy of gun to the K.E. of bullet is $\frac{m}{M}$. Reason: In firing, momentum is conserved. Hence, kinetic energy is in the inverse ratio of masses.

• 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 incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

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

Let's say
Velocity of the bullet = $v_b$
Recoil velocity of the gun = $v_g$
Mass of the bullet = m
Mass of the gun = M
By the principle of conservation of angular momentum, we can write
$m{v}_b=M{v}_g$

$⟹v_g=\frac{m{v}_b}{M}$
lat say x = kinetic energy of the gun

$⟹x=\frac{1}{2}M{v}_g^2=\frac{1}{2}M\frac{m^2{v}_b^2}{M^2}=\frac{1}{2}\frac{m^2{v}_b^2}{M}$
let say y = kinetic energy of the bullet
$y=\frac{1}{2}m{v}_b^2$
we can see
$\frac{x}{y}=\frac{m}{M}$