Question

A body of mass $m_1$ moving with velocity $v$ collides (oblique collision) with a stationary ball of mass $m_2$ get embedded. After the collision , velocity of separation along the line of impact will

• A. be same
• B. decrease $(\ne 0)$
• C. be $\infty$
• D. be zero

Answer 1

The correct option is D be zero

Now $m{u}_1+m_0=m{\overrightarrow{v}}_1+m{\overrightarrow{v}}_2$

$\Rightarrow {\overrightarrow{u}}_1={\overrightarrow{v}}_1+{\overrightarrow{v}}_2⟶\left(1\right)$ vectorial addition

Also since it is elastic collision -

$\Rightarrow \frac{1}{2}m{u}_1^2=\frac{1}{2}m{v}_1^2+\frac{1}{2}{m}_2^2$

$\Rightarrow u_1^2=v_1^2+v_2^2⟶\left(2\right)$

From $\left(1\right)$

$\Rightarrow {\overrightarrow{u}}_1.{\overrightarrow{u}}_1=({\overrightarrow{v}}_1+{\overrightarrow{v}}_2).({\overrightarrow{v}}_1+{\overrightarrow{v}}_2)$

$\Rightarrow u_1^2=v_1^2+v_2^2+2({\overrightarrow{v}}_1.{\overrightarrow{v}}_2)⟶\left(3\right)$

From $\left(2\right)$ and $\left(3\right)$ we get

$\Rightarrow 2{\overrightarrow{v}}_1.{\overrightarrow{v}}_2=0$

$\Rightarrow {\overrightarrow{v}}_1.{\overrightarrow{v}}_2=0$

So, line of impact is zero.

Hence, the answer is zero.