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Question

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 0.1kg/m2 and 10rad/s respectively while those for the second one are 0.2kg/m2 and 5rad/s 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:


A

23J

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B

103J

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C

53J

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D

203J

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Solution

The correct option is D

203J


Step 1: Given

Moment of inertia of first disc: I1=0.1kg/m2

Moment of inertia of second disc: I2=0.2kg/m2

Angular velocity of first disc: ω1=10rad/s

Angular velocity of second disc: ω2=5rad/s

Step 2: Formula Used

The angular velocity of the system will be ω=I1ω1+I2ω2I1+I2

Kinetic Energy of a rotating system: KE=12Iω2

Step 3: Calculate the angular velocity of the entire system using the formula.

ω=0.1×10+0.2×50.1+0.2=1+10.3=20.3=203rad/s

Step 4: Calculate the kinetic energy of the rotation using the formula. The moment of inertia of the entire system will be equal to the sum of moment of inertias.

KE=12Iω2=12I1+I2ω2=120.1+0.22032=12×0.3×4009=203J

Hence, the kinetic energy is 203J.


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