First slide

Rolling motion

Question

A solid sphere is in rolling motion. In rolling motion, the body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t : (K_t+K_r) for the sphere is

Easy

A

7 : 10
B

5 : 7
C

2 : 5
D

10 : 7

Solution

$\large \frac{{K.{E_t}}}{{K.{E_t} + K.{E_r}}} = \frac{{\frac{1}{2}m{v^2}}}{{\frac{1}{2}m{v^2}\left( {1 + \frac{K^2}{R^2} } \right)}}$
$\large =\frac {1}{1+\frac{K^2}{R^2}}=\frac {1}{1+2/5}=\frac 57$

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