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)

# 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)

1. A

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

2. B

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

3. C

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

4. D

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

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### Solution:

$2mR{\omega }^{2}-T=2ma......\left(1\right)$

$T-mR{\omega }^{2}=ma........\left(2\right)$

$\left(1\right)+\left(2\right)⇒mR{\omega }^{2}=3ma$

$a=\frac{R{\omega }^{2}}{3}$

$T-mR{\omega }^{2}=\frac{mR{\omega }^{2}}{3}$

$T=\frac{4}{3}mR{\omega }^{2}$

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