The angular velocity of the disc in the above described case is

\sqrt{\frac{8 g r}{5 [R^{2} + 2 r^{2}]}}

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\sqrt{\frac{6 g r}{5 [R^{2} + 2 r^{2}]}}

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\sqrt{\frac{12 g r}{5 [R^{2} + 2 r^{2}]}}

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\sqrt{\frac{12 g r}{5 R^{2}}}

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Solution

The correct option is C $\sqrt{\frac{12 g r}{5 [R^{2} + 2 r^{2}]}}$
From geometry, $A C^{'} = r s i n 37$
Work-energy theorem, $M g r s i n 37^{o} = \frac{1}{2} I_{O} w^{2}$
$M g r s i n 37^{o} = \frac{1}{2} \times \frac{M}{2} (R^{2} + 2 r^{2}) w^{2}$
$⟹ w = \sqrt{\frac{12 g r}{5 [R^{2} + 2 r^{2}]}}$ $(s i n 37 = .6)$

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Similar questions

In Triangle ABC the value of $\frac{r_{1} + r_{2}}{1 + c o s C}$ is always equal to

r^{2} s q u n i t s

\frac{1}{2} r^{2} s q u n i t s

2 r^{2} s q u n i t s

\sqrt{2} r^{2} s q u n i t s

△ A B C, (r_{2} - r_{1}) (r_{3} - r_{1}) = 2 r_{2} r_{3}

△ A B C

\frac{1}{2}

\sqrt{2}

r^{2} s q u n i t s

\frac{1}{2} r^{2} s q u n i t s

2 r^{2} s q u n i t s

\sqrt{2} r^{2} s q u n i t s

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