Question

A ball of mass 1 kg moving with a velocity of 5 m/s collides elastically with rough ground at an angle $\theta$ with the vertical as shown in figure. What can be the minimum coefficient of friction if ball rebounds vertically after collision? (given tan $\theta =2$)

• A. 3
• B. 1
• C. 4
• D. 5

Answer 1

The correct option is B 1

Given,

$m=1kg$

$tan\theta =2$

From free body diagram,

Impulse momentum theorem,

$\int Ndt=m(v+5cos\theta )$. . . . . . . . .. .(1)

$\int fdt=m5sin\theta$

$\mu \int Ndt=5msin\theta$

$\mu m(v+5cos\theta )=5msin\theta$. . . . . .(2)

According to newton's law of restitution,

$v=35cos\theta$

By solving the above, we get,

$\mu =1$

The correct option is B.