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  • the uniform circular discs are rotating in the same direction around their common axis passing through their centers. The  moment of inertia and angular velocity of the first disc are 

the uniform circular discs are rotating 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 \ kgm^2 and 10 \ rad. s^{-1}  respectively, while those for the second one are 0.2 \ kg.m^2 and 5 \ rad. 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 
Option: 1 \frac{10}{3} \ J
Option: 2 \frac{20}{3} \ J
Option: 3 \frac{2}{3} \ J
Option: 4 \frac{5}{3} \ J

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\\ \text{By angular momentum conservation}\\ I_1 \omega_1+I_2 \omega_2=(I_1+I_2) \omega\\ 0.1 \times 10+ 0.2 \times 5=(0.3) \times \omega\\ \omega=\frac{20}{3}\\ K.E.=\frac{1}{2}I \omega^2=\frac{1}{2}(0.1+0.2) \left[ \frac{20}{3}\right ]^2=\frac{20}{3}J

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