Question

A rigid body of mass M and radius R rolls without slipping on an inclined plane of inclination $\theta$, under gravity. Match the type of body with magnitude of the force of friction.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(a)}& \text{For ring}& \text{(p)}& \frac{Mgsin\theta }{2.5}\\ \text{(b)}& \text{For solid sphere}& \text{(q)}& \frac{Mgsin\theta }{3}\\ \text{(c)}& \text{For solid cylinder}& \text{(r)}& \frac{Mgsin\theta }{3.5}\\ \text{(d)}& \text{For hollow spherical shell}& \text{(s)}& \frac{Mgsin\theta }{2}\end{array}$

• A. A – P; B – Q; C – S; D – S
• B. A – P; B – S; C – Q; D – Q
• C. A – R; B – Q; C – P; D – S
• D. A – S; B – R; C – Q; D – P

Answer 1

The correct option is D

A – S; B – R; C – Q; D – P

$f=\frac{Mgsin\theta }{(1+\frac{m{r}^2}{I})}$

For ring $l=m{r}^2$

$f=\frac{Mgsin\theta }{2}$

for hollow sphere $l=\frac{2}{3}m{r}^2$

$f=\frac{mgsin\theta }{\frac{5}{2}}=\frac{mgsin\theta }{3}$

For solid cylinder, $f=\frac{mgsin\theta }{3}$

For solid sphere, $f=\frac{mgsin\theta }{3.5}$