Question

A solid sphere of mass m and radius r is rolling up the inclined plane of inclination Ф For pure rolling friction force acting on the sphere is

Answer 1

Given info : A solid sphere of mass m and radius r is rolling up the inclined plane of inclination Ф.

To find : for pure rolling , friction force acting on the sphere is ...

solution : let force of friction acting on the solid sphere is Fs

at equilibrium,

mgsinΦ - Fs = ma ...(1)

we know, a = rα , where α is angular acceleration.

torque , τ = I α = Ia/r = Workdone by friction

here I is moment of inertia of solid sphere.

⇒Ia/r = Fs × r

⇒Ia/r² = Fs ....(2)

from equations (1) and (2) we get,

mgsinΦ - Ia/r² = ma

now, a = mgsinΦ/(m + I/r²)

now putting moment of inertia of solid sphere, I = 2/5 mr²

so, a = mgsinΦ/(m + 2/5 mr²/r²) = mgsinΦ/(7/5 m)

= 5/7 gsinΦ

now, friction = Ia/r²

= 2/5 mr² × 5/7 gsinΦ/r²

= 2/7 mgsinΦ

Therefore the force of friction on the solid sphere would be 2/7 mgsinΦ

Answer 2

Answer:

Explanation:

Static friction is your correct ans that I think

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