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

Answer 1

Answer: (D)

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

Answer 2

Velocity of sphere $v=\left[ \frac{M-m}{M+m} \right]u'+\frac{2mu}{m+M}$ Before collision, sphere of mass M remain at rest. Therefore $u'=0$ $v=\frac{2mu}{m+M}=\frac{2u}{1+\frac{M}{m}}$