Question

A ball moving on a horizontal frictionless plane hits an identical ball at rest with a velocity of $50 \, cm \, s^{- 1}$ . If the collision is elastic, calculate the speed imparted to the target ball if the speed of the striking ball after the collision is $30 \, cm \, s^{- 1}$

• A. $20cms^{- 1}$
• B. $30cms^{- 1}$
• C. $40cms^{- 1}$
• D. $50cms^{- 1}$

Answer 1

Answer: (C)

As the collision is perfectly elastic
Hence $\frac{1}{2}mu_{1}^{2}+\frac{1}{2}mu_{2}^{2}=\frac{1}{2}mv_{1}^{2}+\frac{1}{2}mv_{2}^{2}$
$\Rightarrow u_{1}^{2}+u_{2}^{2}=v_{1}^{2}+v_{2}^{2}$
$\left(0.5\right)^{2}+0=\left(0.3\right)^{2}+v_{2}^{2}$
$v_{2}=\sqrt{\left(0.5\right)^{2} - \left(0.3\right)^{2}}$
$v_{2}=40 \, cm \, s^{- 1}$