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 :-
![](https://imagex.cdn.examgoal.net/18hoxe66ijwb5rwev/8e77f5b6-cff5-4a8c-a886-8f0f9161063e/2b79de70-8320-11e9-8081-1d558b7f1d26/file-18hoxe66ijwb5rwew.png)

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: