Question

A bullet weighing 50 gm leaves the gun with a velocity of 30 ms${}^{-1}$. If the recoil speed imparted to the gun is 1 ms${}^{-1}$, the mass of the gun is:

• A. 15 kg
• B. 1.5 kg
• C. 20 kg
• D. 30 kg

Answer 1

The correct option is B 1.5 kg

$\text{Step 1: Apply momentum conservation}$ $\text{[Refer Fig.]}$

For bullet: Mass= $m=50gm$; Velocity =$V=30m/s$

For gun: Mass= $M$; Velocity =$V_0=1m/s$

Since there is no external force acting on the system, linear momentum is conserved. (Considering right direction to be positive)

$P_i=P_f$

$\Rightarrow 0=mV-M{V}_o$

$\Rightarrow M=m\left(\frac{V}{V_o}\right)$

$\text{Step 2: Substituting the values}$

Putting given values:

$M=50gm\times \left(\frac{30m/s}{1m/s}\right)=1500gm$

$\Rightarrow M=1.5kg$

Hence, Option(B) is correct.