First slide

Rolling motion

Question

A hollow sphere of mass m starting from rest rolls down, without slipping, on an inclined plane of inclination $θ$ . What is the total energy of the sphere after 10^-5 s if velocity after 10^-5 s is v?

Moderate

A

$5 / 6 {mv}^{2}$
B

$2 / 3 {mv}^{2}$
C

$10^{- 5} {mv}^{2}$
D

${mv}^{2} / 10^{- 5}$

Solution

$\begin{matrix} Energy = \frac{1}{2} {mv}^{2} + \frac{1}{2} {Iω}^{2} \\ = \frac{1}{2} {mv}^{2} + \frac{1}{2} (\frac{2}{3} {mr}^{2}) \frac{v^{2}}{r^{2}} = \frac{1}{2} {mv}^{2} + \frac{1}{3} {mv}^{2} = \frac{5 {mv}^{2}}{6} \end{matrix}$

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