Question

A body of mass $m$ moving with a velocity $v$ strikes a stationary body of mass $m$ and sticks to it. What is the speed of the system

• A. 2$v$
• B. $v$
• C. $\frac{v}{2}$
• D. $\frac{v}{3}$

Answer 1

The correct option is C $\frac{v}{2}$

Let's consider the velocity of the system after the collision is $v^{\prime }$.

masses of the bodies taken to be, $m_1=m$, $m_2=m$

Initial momentum, $P_i=m_{1}v=mv$

Final momentum, $P_f=(m_1+m_2)v^{\prime }=(m+m)v^{\prime }=2mv$

By using the law of conservation of linear momentum,

$P_i=P_f$

$\Rightarrow mv=2m{v}^{\prime }$

$\Rightarrow v=2v^{\prime }$

$\Rightarrow v^{\prime }=\frac{v}{2}$

The correct option is $\left(C\right)$.