Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centers. The moment of inertia and angular velocity of the first disc are 0.1 kg-m² and 10rad s^-1 respectively while those for second one are 0.2kg-m² and 5rad s^-1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed .The kinetic energy of the combined system is

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$\frac{10}{3} J$

$\frac{20}{3} J$

$\frac{5}{3} J$

$\frac{2}{3} J$

answer is B.

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Detailed Solution

$\begin{array}{l} ω = \frac{I_{1} ω_{1} + I_{2} ω_{2}}{I_{1} + I_{2}} = = \frac{0.1 \times 10 + 0.2 \times 5}{0.1 + 0.2} = \frac{20}{3} rad / s \\ KE = \frac{1}{2} I_{1} ω^{2} + \frac{1}{2} I_{2} ω^{2} = = \frac{1}{2} (0.1 + 0.2) {(\frac{20}{3})}^{2} = = \frac{20}{3} J \end{array}$