A sphere of mass M and radius R is released from the top of an inclined plane of inclination theta .The min coeff of friction btw the plane and the sphere so that it rolls down the plane without sliding is given by?

Question

A sphere of mass M  and radius R is released from the top of an inclined plane of inclination      theta .The min coeff of friction btw the plane and the sphere so that it rolls down the plane without sliding is given by?

mos1635 · Answer

|dw:1333829418859:dw|
to be rolling with out sliding must
V=ω*R
a=α*R
Wx/M=(T*R/I)*R    (T=μ* Ν) (Ν=Wy=M*g*cosθ)
g*sinθ=(μ *g*cosθ*R^2)/Inertia
tanθ=μ*R^2/I
μ=tanθ*Ι/R^2
if given inertia of sfaire I=2/5 Μ R^2
μ=2 tanθ/5Μ