Question

a block of mass m moving at a velocity v collides with another blocks of mass 2 m at rest. the lighter blocks come to rest after collision, find the coefficient of restituation

• A. 1/2
• B. 1
• C. 1/3
• D. 1/4

Answer 1

The correct option is A 1/2

Coefficient of Restitution (COR) is the ratio of the final to initial relative velocity between two objects after they coloid.

$COR\left(e\right)=\frac{Relativevelocityaftercollision}{Relativevelocitybeforecollision}\to \left(1\right)$

At the time of collision,momentum remains constant.

i.e, Momentum before collision=Momentum after constant $\to \left(ii\right)$

A/Q

From $\left(ii\right)$

$mv=\left(2m\right)v^1\Rightarrow v^1=v/2$

From $\left(i\right)$

$e=\frac{R.V_{after}}{R.V_{before}}\Rightarrow r=\frac{v/2}{v}\Rightarrow e=1/2$