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A string is wrapped over the edge of a uniform disc and its free end is fixed to ceiling. The disc move down winding the string with an acceleration of center of mass equal to?

A string is wrapped over the edge of a uniform disc and its free end is fixed to ceiling. The disc move down winding the string with an acceleration of center of mass equal to?

Grade:12th pass

1 Answers

Tushar
19 Points
6 years ago
If the mass and radius of the disc is `M` and ` R`. The moment of inertia will be: MR^2 /2.Let the tension in string is T .As torque = I × (alpha) . Alpha = angular acceleration.T = MR^2/2 × (alpha).Also , F (external) = M× ( acceleration) , of centre of mass,Mg-T = MaAs there is no slipping between rope and disc, a = R× (alpha)By solving the equations, T= ma/2 And Mg = 3Ma /2 Therefore acceleration of centre of mass of the disc will be 2g/3

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