Like a rolling stone

A hollow sphere is released from the top of an inclined plane of inclination θ \theta . What should be minimum coefficient of friction between the sphere and plane to prevent sliding?

Answer is of form k tan \tan θ \theta . Value of k is-

0.1 1 0.3 0.4 0.52 0.2 0.65 0.32

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1 solution

Akshat Sharda
Oct 6, 2016

Note that the axis through the point of contact of the hollow sphere is the instantaneous axis of rotation.

So, about the instantaneous axis of rotation,

m g sin θ R 5 3 m R 2 = f r 2 3 m R 2 f = 2 5 m g sin θ μ m g cos θ μ 2 5 tan θ \frac{mg\sin \theta R}{\frac{5}{3}mR^2}=\frac{fr}{\frac{2}{3}mR^2} \\ f=\frac{2}{5}mg \sin \theta ≤ \mu m g\cos \theta \\ \boxed{\mu ≥ \frac{2}{5} \tan \theta}

Here f f denotes friction force and m m denotes mass of the hollow sphere.

Pls some more expainarion about used formula

Satyam Tripathi - 4 years, 7 months ago

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