Question

A ball of mass $10g$ is dropped on the ground from a height of $10m$. It rebounds to a height of $2.5m$. If the ball is in contact with the ground for $0.01s,$ then which statement is correct?

• A. Impulse force between the ground and a ball is $45N$
• B. Impulse force between the ground and ball is $15\sqrt{2}N$
• C. Coefficient of restitution between the ground and ball is $1/4$
• D. Coefficient of restitution between the ground and ball is $1/2$

Answer 1

Answer: (D)

Coefficient of restitution between the ground and ball is $1/2$

$\begin{array}{c}{v_1}^2=\sqrt{2gH}\\ =\sqrt{2\times 10\times 10}\\ v_1=\sqrt{200}=10\sqrt{2}\\ v_2=\sqrt{2g\times 2.5}\\ \Rightarrow v_2=\sqrt{50}=5\sqrt{2}\\ \Delta P=m{v}_1+m{v}_2\\ =\frac{10}{1000}\left[10\sqrt{2}+5\sqrt{2}\right]\\ =\frac{10}{1000}\times 15\sqrt{2}\\ =\frac{15\sqrt{2}}{100}\\ \therefore F\cdot \Delta T=\Delta P=I\\ I=\frac{15\sqrt{2}}{100}\\ \Rightarrow e=\frac{5\sqrt{2}}{10\sqrt{2}}=\frac{1}{2}\end{array}$

Hence,

option $\left(D\right)$ is correct answer.