First slide

Rolling motion

Question

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :

Easy

A

$1.13 x 10^{- 3} J$
B

$6.25 x 10^{- 4} J$
C

$8.75 x 10^{- 3} J$
D

$8.75 x 10^{- 4} J$

Solution

K.E of the sphere = Translational K.E + Rotational K.E.
$\Rightarrow K E = \frac{1}{2} m v^{2} (1 + \frac{K^{2}}{R^{2}})$ K= Radius of gyration
$\Rightarrow K E = \frac{1}{2} \times 0.5 \times {(\frac{5}{100})}^{2} (1 + \frac{2}{5}) = \frac{35}{4} \times 10^{- 4} J = 8.75 \times 10^{- 4} J$

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