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Q.

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

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a

$6.25 \times 10^{- 4} J$

b

$8.75 \times 10^{- 4} J$

c

$1.13 \times 10^{- 3} J$

d

$8.75 \times 10^{- 3} J$

answer is C.

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Detailed Solution

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$K E_{sphere} = \frac{1}{2} M V_{c m}^{2} + \frac{1}{2} I ω^{2}$

$= \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{5} m r^{2} \times \frac{v^{2}}{r^{2}}$

$= (\frac{1}{2} + \frac{1}{5}) m v^{2}$

$= 8.75 \times 10^{- 4} J$

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