Question

A solid sphere rolls down on an inclined plane. If inclination angle is ${30}^{\circ }$ and friction is sufficient for rolling while not slipping, find $a$ (accelaration) of center of sphere.

• A. $\frac{27}{5}{\text{m/s}}^2$
• B. $\frac{25}{7}{\text{m/s}}^2$
• C. $\frac{7}{25}{\text{m/s}}^2$
• D. $\frac{5}{27}{\text{m/s}}^2$

Answer 1

The correct option is B $\frac{25}{7}{\text{m/s}}^2$

$a=\frac{g\sin \theta }{1+\frac{I}{M{R}^2}}$

$a=\frac{10\times \frac{1}{2}}{1+\frac{2}{5}}=\frac{5}{\frac{7}{5}}=\frac{25}{7}{\text{m/s}}^2$