Question

Two identical balls each moving with speed v at right angle to each other collide perfectly inelastically. The speed after collision is

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

Answer 1

Answer: (D)

$\frac{v}{\sqrt{2}}$

Two identical balls of mass $m$ each moving with velocity $v$ at the right angle to each other collide perfectly inelastically.

Let's consider the velocity of the ball after the collision is $u$.

Applying conservation of linear momentum,

$mv\hat{i}+mv\hat{i}=2m\overrightarrow{u}$

$2\overrightarrow{u}=v\hat{i}+v\hat{j}$

Magnitude, $2u=\sqrt{(v{)}^2+(v{)}^2}=\sqrt{2}v$

$u=\frac{v}{\sqrt{2}}$

The correct option is D.