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Q.

A solid spherical ball is stuck up between two coaxial rotating cylinders as shown whose centers are fixed. There is no slipping anywhere. Find the kinetic energy of the ball (in J). Radius of inner cylinder $= 1 m$ and its angular velocity $ω_{1} = 10 r a d / s$ ; radius of outer cylinder $= 1.5 m$ and it’s angular velocity $ω_{2} = 20 r a d / s$ . Take mass of ball $= \frac{1}{130} k g$ .

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Detailed Solution

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$ω = \frac{ω_{1} r_{1} + ω_{2} r_{2}}{r_{2} - r_{1}} = \frac{10 + 30}{0.5} = 80 r a d / s V_{c} = 10 - 0.25 \times 80 = - 10 m / s k = \frac{1}{2} \times m \times {(10)}^{2} + \frac{1}{2} \times m \times {(\frac{1}{4})}^{2} \times \frac{2}{5} \times 80^{2} k = M \times 130 J$

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