Question

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The ratio $\frac{h_{sph}}{h_{cyl}}$ is given by :

• A. $\frac{14}{15}$
• B. $\frac{4}{5}$
• C. $1$
• D. $\frac{2}{\sqrt{5}}$

Answer 1

Answer: (A)

$\frac{14}{15}$

Answer 2

for solid sphere
$\frac{1}{2} mv^{2} + \frac{1}{2} . \frac{2}{5} mR^{2} . \frac{v^{2}}{R^{2}} =mgh_{sph}$
for solid cylinder
$\frac{1}{2}mv^{2} + \frac{1}{2} . \frac{1}{2} mR^{2} . \frac{v^{2}}{R^{2}} = mgh_{cyl}$
$\Rightarrow \frac{h_{sph}}{h_{cyl}} = \frac{7 /5}{3 /2} = \frac{14}{15}$