First slide

Constraints

Question

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

Difficult

A

$\sqrt{2} mg$
B

mg
C

$\frac{mg}{\sqrt{2}}$
D

2mg

Solution

T sin $45^{0} = ma (for A)$ ----------(i)
mg - T sin $45^{0}$ = ma (for B)--------(ii)
From (i) and (ii), T = $\frac{mg}{2 \sin 45^{0}} = \frac{mg}{\sqrt{2}}$

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