A rough disc of mass m rotates freely with an angular velocity ω . If another rough disc of mass m2 and same radius but spinning in opposite sense with angular speed ω is kept on the first disc. Then:

12mr2×ω-12m2r2×ω=12mr2+14mr2ω'⇒ω'=ω/9d) use work energy principlewf+wg=∆(KE)⇒1234mr2ω2/9-14mr2ω2+18mr2ω2⇒wf+0=-mω2r23

A rough disc of mass m rotates freely with an angular velocity ω . If another rough disc of mass m2 and same radius but spinning in opposite sense with angular speed ω is kept on the first disc. Then:

12mr2×ω-12m2r2×ω=12mr2+14mr2ω'⇒ω'=ω/9d) use work energy principlewf+wg=∆(KE)⇒1234mr2ω2/9-14mr2ω2+18mr2ω2⇒wf+0=-mω2r23

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A rough disc of mass $m$ rotates freely with an angular velocity $ω$ . If another rough disc of mass $\frac{m}{2}$ and same radius but spinning in opposite sense with angular speed $ω$ is kept on the first disc. Then:

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the final angular speed of the disc is $\frac{ω}{3}$

the net work done by friction is zero

the friction does a positive work on the lighter disc

the net work done by friction is $\frac{- m R^{2} ω^{2}}{3}$

answer is A, D.

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$\frac{1}{2} m r^{2} \times ω - \frac{1}{2} \frac{m}{2} r^{2} \times ω = (\frac{1}{2} m r^{2} + \frac{1}{4} m r^{2}) ω'$

$\Rightarrow ω' = ω / 9$

d) use work energy principle

$w_{f} + w_{g} = ∆ (K E) \Rightarrow \frac{1}{2} (\frac{3}{4} m r^{2}) ω^{2} / 9 - [\frac{1}{4} m r^{2} ω^{2} + \frac{1}{8} m r^{2} ω^{2}]$

$\Rightarrow w_{f} + 0 = - m \frac{ω^{2} r^{2}}{3}$

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A rough disc of mass m rotates freely with an angular velocity ω . If another rough disc of mass m2 and same radius but spinning in opposite sense with angular speed ω is kept on the first disc. Then:

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A rough disc of mass $m$ rotates freely with an angular velocity $ω$ . If another rough disc of mass $\frac{m}{2}$ and same radius but spinning in opposite sense with angular speed $ω$ is kept on the first disc. Then: