A ring of mass M and radius R rotating with angular speed ω about a fixed vertical axis passes through ‘O’; with two masses each of mass M8at rest. These can move radially out along two mass less rods as shown. After some time the angular velocity is 8ω9,

If one of them is at 3 R 5 the other is at 4 R 5 , If one of the mass at 2 R 5 the other is at 21 R 5

A ring of mass M and radius R rotating with angular speed ω about a fixed vertical axis passes through ‘O’; with two masses each of mass M8at rest. These can move radially out along two mass less rods as shown. After some time the angular velocity is 8ω9,

L i = MR 2 ω After some time ω 1 = 8 ω 9 r A = 3 R 5 ; r B = ? L ⨍ = MR 2 ω 1 + I A ω 1 + I B ω 1 = MR 2 + M 8 9 R 2 25 + M 8 r B 2 8 ω 9 ∴ L i = L ⨍ ⇒ r = 4 R 5 If OA = 2 R 5 ; OB = r ∴ L i = L ⨍ MR 2 ω = MR 2 + M 8 . 4 R 2 25 + M 8 r 2 8 ω 9 r = 21 R 5

If one of the mass at 3 R 5 the other is at 5 R 4

If one of them is at 3 R 5 the other is at 4 R 5

If one of the mass at 2 R 5 the other is at 21 R 5

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A ring of mass M and radius R rotating with angular speed $ω$ about a fixed vertical axis passes through ‘O’; with two masses each of mass $\frac{M}{8}$ at rest. These can move radially out along two mass less rods as shown. After some time the angular velocity is $\frac{8 ω}{9},$

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If one of the mass at $\frac{3 R}{5}$ the other is at $\frac{5 R}{4}$

If one of them is at $\frac{3 R}{5}$ the other is at $\frac{4 R}{5}$

If one of the mass at $\frac{2 R}{5}$ the other is at $\frac{21 R}{5}$

If one of the mass at $\frac{2 R}{5}$ the other is at $\frac{\sqrt{21} R}{5}$

answer is B, C.

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Detailed Solution

$L_{i} = {MR}^{2} ω$ After some time $ω^{1} = \frac{8 ω}{9} r_{A} = \frac{3 R}{5}; r_{B} = ? L_{⨍} = {MR}^{2} ω^{1} + I_{A} ω^{1} + I_{B} ω^{1}$

$= [{MR}^{2} + \frac{M}{8} \frac{9 R^{2}}{25} + \frac{M}{8} r_{B}^{2}] \frac{8 ω}{9} ∴ L_{i} = L_{⨍} \Rightarrow r = \frac{4 R}{5}$ If

$OA = \frac{2 R}{5}; OB = r ∴ L_{i} = L_{⨍} {MR}^{2} ω = [{MR}^{2} + \frac{M}{8} . \frac{4 R^{2}}{25} + \frac{M}{8} r^{2}] \frac{8 ω}{9} r = \frac{\sqrt{21} R}{5}$

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