A disc is given an initial angular velocity `omega_(0)` and placed on a rough horizontal surface as shown Fig. The quantities which will not depend on the coefficient of friction is/are

Options

A. the time until rolling begins
B. The displacement of the disc until rolling begins
C. the velocity when rolling begins
D. the work done by the force of friction

Answer

C, D

Explanation

Using conservation angular momentum and equation of kinematics `t=(r omega_(0))/(3mug)` so `t` depends on `mu` `s=(omega_(0)^(2)r^(2))/(18 mug)`, if depends on `mu`,
Again at bigning condition `v=0` and `omega=omega_(0)`
both indipendent to `mu`
Again work by friction
`W_((f))=-mumgrxx theta_("slipping")=-mugr`
`(omega^(2)r^(2))/(2 mug)=(omega^(2)r^(2))/(2)`
Thus it is independent to `mu`