Question

A table with smooth horizontal surface is placed in a 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 a string going over the pulley. Initially the masses are held by a person with the string 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 and the tension in the string.
Figure

Answer 1

Explanation:

Since, we have to discover the Acceleration and Tension regarding the Cabin at that point thought about that we are sitting in the Non-Inertial Frame of the Reference. Presently, If we were in the lodge, at that point we will feel the outward power outside.  

There must be the Centripetal Force on the majority joined with the Pulleys.  

Give the Tension access the Masses be 'T' and speeding up be 'a'.  

Presently, Let us accept that the mass m is going upwards and mass 2m is going downwards. Additionally, Centrifugal power equivalent to mω²R will be acting outwards on the two masses.  

In mass m, (m₁),

$\begin{equation}\begin{aligned}&T-\mathrm{m} \omega^{2} \mathrm{R}=\mathrm{ma}\\&T=m \omega^{2} R+m a\end{aligned}$

Similarly, In mass 2m,

$\begin{equation}\begin{aligned}&2 \mathrm{m} \omega^{2} \mathrm{R}-\mathrm{T}=2 \mathrm{ma}\\&T=2 \mathrm{m} \omega^{2} \mathrm{R}-2 \mathrm{ma}\end{aligned}$

On solving, it we will get,

$\begin{equation}a=\frac{\omega^{2} R}{3}$  and  $\begin{equation}T=\frac{4 m \omega^{2} R}{3}$

Answer 2

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Please refer the above attachment