A hollow sphere of mass m and radius  R is rolling downward on a rough inclined plane of inclination  0 (theta) . if the coefficient of friction between  the hollow sphere and incline is µ then
1. Friction opposes its translation
2. Friction supports rotation motion
3. on decreasing  0 (theta), frictional force decreases
4. all of these.
Pleae provide justification

Asked by Sayoni Maiti | 13th Oct, 2014, 12:21: AM

Expert Answer:

The answer to this is 4.all of these.

When a body is placed on an inclined plane at an angle θ, it tries to slip down and hence a static friction 'f' acts upwards. Thus it opposes the translational motion. This friction provides a torque which causes the body to rotate.Frictionaforce providethe torque for rotation. Hence we can say that the friction supports rotational motion.
If μ is the minimum coefficient of friction between  the hollow sphere and the incline plane .From the motion of hollow sphere we can write that
mg sin θ - f =ma
where a is the acceleration along the incline plane(i.e. tangential acceleration of the rolling sphere)
f - static friction acting upwards
θ- inclination angle.
From all the above we can say that the frictional force decreases on decreasing θ.

Answered by Jyothi Nair | 13th Oct, 2014, 11:14: AM

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