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Rotational Dynamics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsRotational Dynamics2 Marks
Question
A ring and a disc having the same mass roll on a horizontal surface without slipping with the same linear velocity. If the total KE of the ring is $8 \mathrm{~J}$, what is the total KE of the disc?
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Answer

Data : $M_{\text {ring }}=M_{\text {disc }}=M, v_{\text {ring }}=v_{\text {disc }}=v, E_{\text {ring }}=8 \mathrm{~J}$
The total kinetic energies of rolling without slipping on a horizontal surface,
$\mathrm{E}_{\text {ring }}=\mathrm{Mv}^2$ and $\mathrm{E}_{\mathrm{disc}}=\frac{3}{4} M v^2$
since they have the same mass and linear velocity.
$\therefore \mathrm{E}_{\text {disc }}=\frac{3}{4} \mathrm{E}_{\text {ring }}=\frac{3}{4} \times 8=6 \mathrm{~J}$

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