Question

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 then 1. Friction opposes its translation 2. Friction supports rotation motion 3. On decreasing 0 (theta), frictional force decreases 4. All of these.

Answer 1

Answer:

ANSWER

f is the frictional force is upward direction along inclined plane.

α is the angular acceleration of the sphere.

Moment of inertia of the sphere about centre of mass is I=

5

2

mR

2

.N is the normal reactional force on the sphere &N =mgcosθ

f=μN=μmgcosθ

Torque about centre of mass sphere is

Iα=f.R

For downward motion let the acceleration along inclined plane α

So, mgsinθ−f=ma

for pure rotation α=

R

a

So, mgsinθ−f=mαR

⟹mgsinθ=f+

2

5

f

⟹mgsinθ=

2

7

f

⟹

2

7

μmgcosθ=mgsinθ

⟹μ=

7

2

tanθ

This is the minimum coefficient of friction So, it should be

μ≥

7

2

tanθ