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Two discs of moment of inertia I(1) and ...

Two discs of moment of inertia `I_(1)` and `I_(2)` and angular speeds `omega_(1)` and `omega_(2)` are rotating along the collinear axes passing through their center of mass and perpendicular to their plane. If the two are made to rotate combindly along the same axis the rotational `K.E.` of system will be

A

(a)`(I_1omega_1+I_2omega_2)/(2(I_1+I_2)`

B

(b)`((I_1+I_2)(omega_1+omega_2)^2)/2`

C

(c)`((I_1omega_1+I_2omega_2)^2)/(2(I_1+I_2)`

D

(d)None of these

Text Solution

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To solve the problem of finding the rotational kinetic energy of a system of two discs rotating along the same axis, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the System**: We have two discs with moments of inertia \( I_1 \) and \( I_2 \), and they are rotating with angular speeds \( \omega_1 \) and \( \omega_2 \) respectively. 2. **Conservation of Angular Momentum**: ...
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