Question

A body of radius $R$ and mass $m$ is rolling smoothly with speed $v$ on a horizontal surface. It then rolls up a hill to a maximum height h. If $h=\frac{3v^2}{4g}$,what might the body be?

• A. a solid circular cylinder
• B. a hollow circular sphere
• C. a solid circular sphere
• D. a hollow circular cylinder

Answer 1

The correct option is A a solid circular cylinder

Given, maximum height, $h=\frac{3v^2}{4g}$
According mechanical energy conservation
$U_i+K_i=U_f+K_f,$
$0+\frac{1}{2}m{v}_{cm}^2+\frac{1}{2}I\omega =mgh+0$
$\Rightarrow \frac{1}{2}m{v}^2+\frac{1}{2}I{\left(\frac{v}{R}\right)}^2=mg\left(\frac{3v^2}{4g}\right)$
$\Rightarrow I=\frac{1}{2}m{R}^2$
This is the moment of inertia for a solid cylinder.

Final answer:(a)