Question

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

Answer 1

$Mg-\frac{T}{\sqrt{2}}=m{q}_1$
$\frac{T}{\sqrt{2}}=m{q}_2$
Also story is ininextensible
$\therefore$ ace story is same
$\therefore \frac{a_1}{\sqrt{2}}=\frac{a_2}{\sqrt{2}}$
$⟹a_1=a_2⟹a$
$\therefore Mg-\frac{I}{\sqrt{2}}=ma$
$=\frac{I}{\sqrt{2}}⟹ma$
$\therefore Mg-\frac{I}{\sqrt{2}}=\frac{I}{\sqrt{2}}$
$T=\frac{MI}{\sqrt{2}}$