Question

A solid sphere rolls down without slipping from rest on a ${30}^{\circ }$ incline. Its linear acceleration is

• A. $5g/7$
• B. $5g/14$
• C. $2g/3$
• D. $g/3$

Answer 1

The correct option is A $5g/7$

$I=\frac{2}{5}m{R}^2$
Net force along the incline $=mg\sin \theta -f$
$ma=mg\sin \theta -f\to \left(1\right)$
angular acceleration, $f\times R=I\propto$ and $\alpha =\frac{a}{R}$
$\Rightarrow f=\frac{2}{5}ma\to \left(2\right)$
Putting (2) in (1)
$\Rightarrow a=\frac{5}{7}g\sin \theta$.