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  4. Beads A and B each of mass m, are connected by a light inextensible cord. They are constrained (restricted) to move on a frictionless ring in a vertical plane as shown. The beads are released from rest at the position shown. The tension in the cord just after the release is <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/7b1550feca58d7e75964cb9c9b542c53-.png />

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Q. Beads $A$ and $B$ each of mass $m$, are connected by a light inextensible cord. They are constrained (restricted) to move on a frictionless ring in a vertical plane as shown. The beads are released from rest at the position shown. The tension in the cord just after the release is
image

Laws of Motion

Solution:

image
$T\,sin\,45^{\circ}=ma$ (for A) .....(i)
$Mg-T\,sin\,45^{\circ}=ma$ (for B) .....(ii)
From (i) and (ii), $T=\frac{mg}{2\,sin\,45^{\circ}}$
$ = \frac{mg}{\sqrt{2}}$