Question

Suppose a solid cylinder of radius R is caused to rotate with a torque of known magnitude about an axis through its center. The same torque is then applied to a hollow cylinder of outer radius R and inner radius r. If their masses are equal, which object has the greater angular acceleration?

A. The solid cylinder has greater angular acceleration.

B. Both cylinders have the same acceleration

C. The hollow cylinder has a grater angular acceleration

Answer 1

Since, Torque() = I*

where, = angular acceleration

I = moment of inertia

So, = /I

s/h = (s/h)*(Ih/Is)

given,

Torque on solid sphere(s) = Torque on hollow sphere(h)

Is = moment of inertia of Solid cylinder = 0.5*M*R^2

Ih = moment of inertia of Hollow cylinder = M*R^2

So, s/h = 1*(M*R^2)/(0.5*M*R^2) = 2

s = 2*h

angular acceleration of the solid cylinder has greater angular acceleration than the hollow cylinder.

Therefore correct option is A.