An ideal string is wrapped on a ring and the free end of the string is attached to the ceiling as shown in the figure. Initially, the system is held in equilibrium by an external agent and at some instant of time, the system is released from rest. If there is no slipping between the string and the ring, then the tension in the string is

• A

  $mg$
• Correct answer
  B

  $\frac{mg}{2}$
• C

  $\frac{mg}{3}$
• D

  $2mg$

Solution

$mg-T=ma$

$TR=m{R}^2\alpha$

$a=\alpha R$

$\frac{mg-T}{m}=\frac{T}{m}$

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

Hence, the correct answer is option: 'B'.