Question

A hollow cylinder is rolling on an inclined plane, inclined at an angle of ${30}^o$ to the horizontal. Its speed after travelling a distance of 10 m will be

• A. 49 m/sec
• B. 0.7 m/sec
• C. 7 m/sec
• D. Zero

Answer 1

The correct option is C 7 m/sec

The distance of 10 m on the hypotenuse on an incline of ${30}^0$ corresponds to a height difference of 5. Thus change in potential energy is given as $5mg$.
The change in the kinetic energy is given as
$\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^2$
moment of inertia of a hollow cylinder about centroidal axis is $m{r}^2$
Thus we get the kinetic energy as
$\frac{1}{2}m{v}^2+\frac{1}{2}m{r}^2\frac{v^2}{r^2}$
or
$m{v}^2$
Equating both the energies we get
$5mg=m{v}^2$
or
$v=\sqrt{49}=7m/s$