Question

Two identical balls of equal masses A and B are lying on a smooth surface as shown in figure. Ball A hits the ball B (which is at rest) with a velocity v$=$ 16 m/s. What should be the minimum value of coefficient of restitution between A and B so that B just reaches the highest point of inclined plane : $(g=10m/s^2)$

• A. $\frac{2}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is D $\frac{1}{4}$

By momentum conservation
$16=V_A+V_B......\left(1\right)$
$16e=V_B-V_A......\left(2\right)$
from (1) and (2)
$V_B=8(e+1)$
As $V_B=\sqrt{2gH}$
$8(e+1)=\sqrt{2gH}\therefore e=1/4.$