Question

Two small beads P and Q of equal mass ( = m) are connected by a light inextensible string. They are constrained to move on a frictionless ring in a vertical plane. The blocks are released from rest as shown in the figure. The tension in the string just after release is

• A. $\frac{mg}{\sqrt{2}}$
• B. $\frac{mg}{\sqrt{3}}$
• C. $\frac{2}{\sqrt{3}}mg$
• D. $\frac{\sqrt{3}}{2}mg$

Answer 1

The correct option is A $\frac{mg}{\sqrt{2}}$

FBD's just after release are
$mg-Tcos{45}^{\circ }=ma$
$Tsin{45}^{\circ }=ma$
$T=\sqrt{2}ma$ .....(1)
$mg-\sqrt{2}ma.\frac{1}{\sqrt{2}}=ma........Fromeqn\left(1\right)$
$mg=2maora=\frac{g}{2}$
$\therefore T=\sqrt{2}m.\frac{g}{2}=\frac{mg}{\sqrt{2}}$