Question 270: 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 h
sph
and h
cyl
on the incline. The ratio
h
sph
/h
cyl
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 h sph and h cyl on the incline. The ratio h sph /h cyl is given by :-

Choose the correct answer: