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Q.

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg – m2 and 10 rad s-1 respectively while those for the second one are 0.2 kg-m2 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:

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a

103J

b

23J

c

53J

d

203J

answer is D.

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Detailed Solution

After they stuck, let they move with angular velocity  ω. By conserving Angular momentumI1ω1+I2ω2=I1+I2ω ⇒ω=I1ω+I2ω2I1+I2=0.110+0.250.1+0.2=203 rad/s KE of system  =12I1+I2ω2=120.1+0.22032=203J
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