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A table with smooth horizontal surface is placed in a cabin which moves in circle of a large radius R. A smooth pulley of small radius is fastened to the table Two masses m and 2m placed on the table are connected through string over the pulley Initially the masses are held by a person with the string along the outwards radius and then the system is released (with respect to the cabin)

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The magnitude of the initial acceleration of the masses as seen from the cabin is $\frac{ω^{2} R}{2}$

The tension in the string is $\frac{4}{3} m ω^{2} R$

The tension in the string is $\frac{2}{3} m ω^{2} R$

The magnitude of the initial acceleration of the masses as seen from the cabin is $\frac{ω^{2} R}{3}$

answer is A, D.

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Detailed Solution

$2 m R ω^{2} - T = 2 m a ...... (1)$

$T - m R ω^{2} = m a ........ (2)$

$(1) + (2) \Rightarrow m R ω^{2} = 3 m a$

$a = \frac{R ω^{2}}{3}$

$T - m R ω^{2} = \frac{m R ω^{2}}{3}$

$T = \frac{4}{3} m R ω^{2}$

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