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System Of Particles And Rotational Motion

Question
CBSEENPH11020398

A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is

  • fraction numerator straight g space sin space straight theta over denominator 1 space plus space straight I divided by MR squared end fraction
  • fraction numerator straight g space sin space straight theta over denominator 1 plus space MR squared divided by straight I end fraction
  • fraction numerator straight g space sin space straight theta over denominator 1 minus straight I divided by MR squared end fraction
  • fraction numerator straight g space sin space straight theta over denominator 1 minus MR squared divided by straight I end fraction

Solution

A.

fraction numerator straight g space sin space straight theta over denominator 1 space plus space straight I divided by MR squared end fraction
Mg space sin space straight theta space minus space straight f space equals space Ma
fR space equals space straight I straight a over straight R
rightwards double arrow space straight a space equals space fraction numerator straight g space sin space straight theta over denominator open parentheses 1 plus begin display style straight I over MR squared end style close parentheses end fraction