Question

A solid sphere has linear velocity `v_(0)=4` m/s and angular velocity `omega_(0)=9` rad/s as shown. Ground on which it is moving , is smooth . It collides elastically with a rough wall of coefficient of friction `mu` . Radius of the sphere is 1m and mass is 2 kg .

If the sphere after colliding with the wall rolls without slipping on opposite direction, then coefdicient of friction `mu` is
A. `(1)/(2)`
B. `(2)/(3)`
C. `(1)/(3)`
D. `(1)/(4)`

Answer 1

Correct Answer - D

Answer 2

Answer: (D)

By impulse-momentum theorem

\(N\Delta t=(+8)-(-8)\)

\(N\Delta t=16-----(i)\)

By angular impulse - angular momentum theorem

\(-\mu N\Delta t=\frac{2}{5}\times2(1)^2(4-9)\)

\(-16\mu=\frac{4}{5}\times(-5)\)

\(\mu=\frac{1}{4}\)