Question

Two objects A and B, each of mass m,are connected by a light inextensible string. They are restricted to move on a frictionless ring of radius R in a vertical plane. The objects are released from rest at the position shown in figure. Then, the tension in the cord just after release is:

• A. $Zero$
• B. $mg$
• C. $\sqrt{2}mg$
• D. $mg/\sqrt{2}$

Answer 1

The correct option is D $mg/\sqrt{2}$

directions of 'a' and 'b' are different but the magnitude of 'a' and 'b' are the same.

Since the length of the rope AB is same

$\begin{array}{c}a\cos 45=b\cos 45\\ a=b\\ AlsoT\sin 45=mb..................\left(1\right)forA\\ mg-T\sin 45=ma...............\left(2\right)forB\\ 2ma=mg=>a=\frac{g}{2}\\ substitutingin\left(1\right)\\ \frac{T}{\sqrt{2}}=\frac{mg}{2}\\ T=\frac{mg}{\sqrt{2}}\end{array}$

Hence,

Option $D$ is correct.