Question

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

• 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. $\frac{g\,sin\,\theta}{1-\frac{MR^{2}}{I}}$

Answer 1

Answer: (A)

$\frac{g\,sin\,\theta}{1+\frac{I}{MR^{2}}}$

Answer 2

$Mg\,sin\,\theta-f=Ma$ $fR=I \frac{a}{R}$ $\Rightarrow a=\frac{g\,sin\,\theta}{\left(1+\frac{I}{MR^{2}}\right)}$