First slide

Newton's laws of motion

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 (as shown in the figure). The objects are released from rest at the position shown. Then the tension in the cord just after release is

Difficult

A

Zero
B

mg
C

$\sqrt{2}$ mg
D

mg/ $\sqrt{2}$

Solution

As shown in Figs. (a) and (b) from FBD of A,
$T \cos 45^{\circ} = m a . . . . . . (i)$
From FBD of .B:
$M g - T \cos 45^{\circ} = m a . . . . . (i i)$
From (i) and (ii), we get $T = m g / \sqrt{2}$

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