Question

A sphere rolling on a horizontal rough surface collides elastically with a smooth vertical wall, as shown in Figure. State which of the following statements is true or false.
After collision the friction the linear force acts on the sphere such that it decreases the linear speed and increases the angular speed.

Answer 1

R.E.F image

after collision the velocity reverses

$\mu mg=ma$

$a=\mu g$

(1) acceleration is opposite to velocity speed decrease

angular momentum = mvr

(2) magnitude of angular momentum decreases

when it again rdls $V_f=w_{f}R$ not $V=wR$ uniformly

$(V-\mu gt)=(-w+\alpha t)R$ $I=\mu mgR=I\alpha$

$wRV-\mu gt=(-w+\frac{5}{2}\frac{\mu gt}{R})R$ $=\frac{2}{5}m{R}^2\alpha$

$t=\frac{4}{7}\frac{wR}{\mu g}$ $\alpha =\frac{5}{2}\frac{\mu g}{R}$

$V_f=V-\mu gt$

$=aR-\frac{4}{7}\frac{aR}{\mu g}$

$V_f=\frac{3}{7}wR$

$w_f=\frac{V_f}{R}$

$w_f=\frac{3}{7}w$