Q. A round uniform body of radius $R$, mass $M$ and moment of inertia $I$, rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is
A) $\frac{g\sin\theta}{1 + \frac{I}{MR^{2}}}$
B) $\frac{g\sin\theta}{1 + \frac{MR^{2}}{I}}$
C) $\frac{g\sin\theta}{1 - \frac{I}{MR^{2}}}$
D) $\frac{g\sin\theta}{1 - \frac{MR^{2}}{I}}$
Explanation
(a) $Mg\sin{\theta - f = Ma}$
$fR = I\frac{a}{R} \Rightarrow \ a = \frac{g\sin\theta}{\left( 1 + \frac{I}{MR^{2}} \right)}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.