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

• A. zero
• B. mg
• C.
• D.

Answer 1

The correct option is D

At the instant shown (when both masses are released) A will move horizontally towards left and B moves vertically downwards.

Now, let's draw free body diagrams for A & B,

From newton's law,

For A (Horizontal forces) & for B (vertical forces)

T sin${45}^{\circ }$ = $m_a$$a_a$ ....(i)

mg - T sin${45}^{\circ }$ = $m_b$$a_b$ ....(ii)

Also if A moves x from initial position along the ring then B is bound to cover same x units along the ring $\Rightarrow$ $a_A$ = $a_B$ ....(iii)

$\therefore$ from (i), (ii) & (iii)

T=$\frac{mg}{\sqrt{2}}$