Question

A cylinder of radius `R` and mass `M` rolls without slipping down a plane inclined at an angle `theta`. Coeff. of friction between the cylinder and the plane is `mu`. For what maximum inclination `theta`, the cylinder rolls without slipping ?
A. `tan^(-1) mu`
B. `tan^(-1) (3mu)`
C. `tan^(-1) 2mu`
D. `tan^(-1) .(3)/(2) mu`

Answer 1

Correct Answer - B
As is know from theory,
`mu = (tan theta)/(1 + mR^(2)//I) = (tan theta)/(1+2) = (tan theta)/(3)`
`tan theta_(max) = 3mu`
`theta_(max) = tan^(-1) (3mu)`