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AP EAMCET20226 Jul 2022Evening ShiftPhysicsRotational MotionActual

A block of mass m is hanging by a rope tied to a rotating solid disc of mass M and radius R as shown in the figure. If is the angular acceleration of the disc, then the linear acceleration of the block is ( g = acceleration due to gravity)

Options

  1. Am m+M g
  2. Bm 2 m+M g
  3. Cm m+ M 2 g
  4. D2 m m+M g

Correct answer

C. m m+ M 2 g

Step-by-step solution

The given situation is shown below If a be the acceleration of block, then by equation of motion. m g-T=m a...(i) We know that, torque ( ) in the disc =I T R= M R^2 2 ( =T R . and .I= M R^2 2 ) T= M R 2 ...(ii) From Eqs. (i) and (ii), we get aligned & m g- M R 2 =m a & m g- M R 2 a R =m a m g- m a 2 =m a & m g= m a 2 +m a m g= ( M 2 +m ) a & a= m g m+ M 2 aligned

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