Question

A string is wrapped over the curved surface of a uniform solid cylinder and the free end is fixed with rigid support. The solid cylinder moves down, unwinding the string. Find the downward acceleration of the solid cylinder.

Answer 1

mass and radius of the disc is `M` and ` R`

moment of inertia will be: MR^2 /2.

tension in string is T .

torque = I × (alpha)

Alpha = angular acceleration.

T = MR^2/2 × (alpha).

Also , F (external) = M× ( acceleration)

Mg-T = Mass between rope and disc,

a = R× (alpha)

the equations, T= ma/2 And Mg = 3Ma /2

acceleration of centre of mass will be 2g/3