Question

A gun fires a shell and recoils horizontally. if the shell travels along the barrel with speed $v$, the ratio of speeds with which the gun recoils, if the barrel is (i) horizontal (ii) inclined at an angle of ${30}^{\circ }$ with horizontal, is

• A. $1$
• B. $\frac{2}{\sqrt{3}}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{2}{\sqrt{3}}$

Let velocity of the shell is $v$ and mass is $m$ and velocity of the gun is $v_1$ in case of horizontally fired and $v_2$ when inclined with horizontal and mass is $M$.
Case 1: When fired horizontally
$\therefore mv=M{v}_1$
$\therefore v_1=\frac{mv}{M}$ ...(i)
Case 2: When inclined with horizontal
$mv\cos {30}^{\circ }=M{v}_2$
$\therefore v_2=\frac{\sqrt{3}mv}{2M}$ ...(ii)
From equation (i) and (ii) we get, $\frac{v_1}{v_2}=\frac{2}{\sqrt{3}}$
$\therefore \left(b\right)$ .