Question

A bag of sand of mass $m$ is suspended by a rope. A bullet of mass $\left(\frac{m}{n}\right)$ is fired at it with a velocity $V$ and gets embedded into it. The velocity of the bag finally is :

• A. $\frac{V}{n}$
• B. $\frac{V}{n+1}$
• C. $\frac{nV}{n+1}$
• D. $\frac{V}{n}\times (n+1)$

Answer 1

The correct option is B $\frac{V}{n+1}$

Given
$m_1=\frac{m}{n}$
$m_2=m$
$u_1=V$
$u_2=0$
Let, $V^{\prime }$ be the velocity of the of the bag finally.
Here, the bullet get embedded into bag after collision hence, collision is perfectly inelastic.
$m_1{u}_1+m_2{u}_2=(m_1+m_2)V^{\prime }$
$\frac{m}{n}\left(V\right)+m\left(0\right)=(\frac{m}{n}+m)V^{\prime }$
$\frac{m}{n}\left(V\right)=\frac{m(n+1)}{n}{V}^{\prime }$
$V^{\prime }=\frac{\frac{m}{n}\left(V\right)}{\frac{m(n+1)}{n}}$
$V^{\prime }=\frac{V}{n+1}$