Question 276: Centre of Mass and Rotational Motion

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 hsph and hcyl on the incline. The ratio
hsph/hcyl is given by :-

Accepted Answer

For solid sphere
$${1 \over 2}m{v^2} + {1 \over 2}.{2 \over 5}m{R^2}.{{{v^2}} \over {{R^2}}} = mg{h_{sph}}$$
For solid cylinder
$${1 \over 2}m{v^2} + {1 \over 2}.{1 \over 2}m{R^2}.{{{v^2}} \over {{R^2}}} = mg{h_{cyl}}$$
$$ \Rightarrow {{{h_{sph}}} \over {{h_{cyl}}}} = {{7/5} \over {3/2}} = {{14} \over {15}}$$

Answer

1

Answer

14/15

Answer

4/5

Answer

2/$$\sqrt5$$

Centre of Mass and Rotational Motion

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 hsph and hcyl on the incline. The ratio hsph/hcyl is given by :-

Choose the correct answer: