Question

A spherical shell of radius R is rolling down an incline of inclination θ without slipping. Find minimum value of coefficient of friction.

• A. $\frac { 2 } { 7 }$ tanθ
• B. $\frac { 2 } { 5 } \tan \theta$
• C. $\frac { 2 } { 3 } \tan \theta$
• D. None

Answer 1

Answer: (B)

$\frac { 2 } { 5 } \tan \theta$

Answer 2

F_r r = Iα

or μmg cos θ = $\frac { 2 } { 3 } \mathrm { Ma }$

μmg cos θ = $\frac { 2 } { 3 } M \frac { g \sin \theta } { 1 + ( 2 / 3 ) } = \mu = \frac { 2 } { 5 } \tan \theta$ Shortcut

μ = $\frac { \left( \mathrm { I } / \mathrm { MR } ^ { 2 } \right) \tan \theta } { 1 + \left( \mathrm { I } / \mathrm { MR } ^ { 2 } \right) } = \frac { 2 } { 5 } \tan \theta$