Question

A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius R with $\omega$. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the strings along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin.

• A. R
• B. 3R
• C.
• D.

Answer 1

The correct option is C

So the cabin is going in a circle. Let's go in the cabin's frame. So now that we are in the cabin which is a non-inertial frame (newton's laws not valid) so we subtract our acceleration from every thing else in the cabin. I hope you remember all this.

So I am going with same $\omega$ as cabin so my centripetal acceleration will be ${\omega }^2$ R towards centre so I will subtract this from the blocks.

Let's draw the free body diagram of blocks.

Oh wait it is very similar to the case when the pulley block system is kept on earth.
From the above F.B.D
$T-ma-m{\omega }^{2}R=0\to \left(1\right)$
$T+2ma-2m{\omega }^{2}R=0\to \left(2\right)$
Eqn(1) - Eqn(2) gives
$\Rightarrow 3ma=m{\omega }^{2}R$
$\Rightarrow a=\frac{{\omega }^{2}R}{3}$