Question

An object of mass $m$ is moving with velocity $\overrightarrow{u}$ towards a plane mirror kept on a stand as shown in the figure. The mass of the mirror and stand system is $m$. A head-on elastic collision takes place between the object and the mirror stand, the velocity of image before and after the collision is

• A. $\overrightarrow{u},\overrightarrow{2u}$
• B. $-\overrightarrow{u},-\overrightarrow{2u}$
• C. $-\overrightarrow{u},\overrightarrow{2u}$
• D. $\overrightarrow{u},-\overrightarrow{2u}$

Answer 1

The correct option is C $-\overrightarrow{u},\overrightarrow{2u}$

We know that in a plance mirror, object distance = image distance
Before collision
$\therefore {\overrightarrow{V}}_{\text{image}}=-{\overrightarrow{V}}_{\text{object}}=-\overrightarrow{u}$

Now after headon elastic collision, mirror will move with velocity $\overrightarrow{u}$ and object will have zero velocity and we know in this case when mirror moves and object is stationary, image moves with twice as velocity as of mirror i.e. $\overrightarrow{2u}$
After collision,
${\overrightarrow{V}}_{\text{image}}=\overrightarrow{2u}$
$\therefore \left(c\right)$ is the correct option.