Question

A sphere rolls down on an inclined plane of inclination $\theta$. What is the acceleration as the sphere reaches bottom?

• A. $\frac{5}{7}g\sin \theta$
• B. $\frac{3}{5}g\sin \theta$
• C. $\frac{2}{7}g\sin \theta$
• D. $\frac{2}{5}g\sin \theta$

Answer 1

The correct option is A $\frac{5}{7}g\sin \theta$

Net force = $mg\sin \theta$

Friction force = $F(\uparrow )$

For linear motion,

$mg\sin \theta =f=mg$ ...(1)

angular motion

$fR=I\alpha$ .... (2)

$\therefore mg\sin \theta =ma+\frac{I\alpha }{R}$ ....(3)

$a=\alpha R$

$\therefore a=\frac{59}{7}\sin \theta$