Question

A hollow sphere rolls down a 30 degree incline of length 6m without slipping . The speed of centre of mass at the bottom of plane is

Answer 1

Answer:

6

Explanation:

Given A hollow sphere rolls down a 30 degree incline of length 6m without slipping . The speed of centre of mass at the bottom of plane is

We know that

By work energy theorem and by downward force,

K.E final – K.E initial = mgl sinθ (at initial condition K. E will be 0 at rest)

1/2 mv^2 (centre of mass = cm) + 1/2 I (centre of mass) ω^2 = mgl sin θ

We know that ω = V cm / R  for rolling since slipping is zero.

So 1/2 mv^2 + 1/2 (2/3 mR^2) Vcm^2 / R^2  = mgl sin θ(for hollow sphere)

1/2 Vm^2 (1 + 2/3) = gl sinθ

So gl sinθ = Vm^2 / 2(5/3)

So Vcm = √6 gl sinθ / 5

             = √ 6 x 10 x 6 sin 30 / 5

            = √150 / 5

             = 6 m/s