Question

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is

• A. $\frac{2uM}{m}$
• B. $\frac{2um}{M}$
• C. $\frac{2u}{1 + \frac{m}{M}}$
• D. $\frac{2u}{1 + \frac{M}{m}}$

Answer 1

Answer: (C)

$\frac{2u}{1 + \frac{m}{M}}$

Answer 2

Final velocity of the target

$v_{2} = \left( \frac{m_{2} - m_{1}}{m_{1} + m_{2}} \right)u_{2} + \frac{2m_{1}u_{1}}{m_{1} + m_{2}}$

As initially target is at rest so by substituting $u_{2} = 0$ we get $v_{2} = \frac{2Mu}{M + m} = \frac{2u}{1 + \frac{m}{M}}$.