Question

A car having a mass $M$ collides with a stationary bike, having a mass one-fourth of that of the car, and comes to a stop. If the car was travelling at a speed of $V$, find the final velocity of the bike.(Neglect friction during collision)

• A. $2V$
• B. $\frac{V}{2}$
• C. $4V$
• D. $\frac{V}{4}$

Answer 1

The correct option is C $4V$

Let the mass and velocity of the bike be $m$ and $v$ respectively.

Given: mass of car $=M$, velocity of car $=V$,
mass of bike, $m=\frac{M}{4}$.
Inital momentum of bike = $0$ (B is initally at rest)
Inital momentum of car = $MV$
Final momentum of car = $0$ (A comes to rest after collision)
Final momentum of bike = $mv$

Using the law of conservation of momentum:
When no external force acts on the system,
Initial momentum = Final momentum.
$MV+0=0+mv\Rightarrow v=\frac{MV}{m}=\frac{MV}{\frac{M}{4}}$
$\Rightarrow v=4V$
Therefore, the final velocity of bike is $4V$.