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Q.

Consider an idealized case of rolling of solid ball in which bottom most point P rotates on circular path shown by dotted line in the figure. Radius of circular path is half of radius of sphere. Ball rolls without sliding with its center moving with speed $v_{0} = \sqrt{\frac{5}{13}} m / s$ . Calculate kinetic energy of ball in joule if mass of ball is M = 4 kg.

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Detailed Solution

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$\begin{array}{l} V_{0} = \frac{R}{2} ω_{0} \\ ω_{0} = \frac{2 V_{0}}{R} \\ K \cdot E = \frac{1}{2} {MV}_{0}^{2} + \frac{1}{2} \cdot \frac{2}{5} {MR}^{2} \frac{4 V_{0}^{2}}{R^{2}} \\ = [\frac{1}{2} + \frac{4}{5}] {MV}_{0}^{2} = \frac{13}{10} {MV}_{0}^{2} = \frac{13}{10} \times 4 \times \frac{5}{13} = 2 J \end{array}$

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Consider an idealized case of rolling of solid ball in which bottom most point P rotates on circular path shown by dotted line in the figure. Radius of circular path is half of radius of sphere. Ball rolls without sliding with its center moving with speed v0=513m/s . Calculate kinetic energy of ball in joule if mass of ball is M = 4 kg.