In the given figure a ring of mass m is kept on a horizontal surface while a body of equal mass m is attached through a string, which is wound on the ring. When the system is released the ring rolls w

Question

In the given figure a ring of mass m is kept on a horizontal surface while a body of equal mass m is attached through a string, which is wound on the ring. When the system is released the ring rolls without slipping. Consider the following statements and choose the correct option.

(i) Acceleration of the centre of mass of the ring is $\frac{g}{3}$

(ii) Acceleration of the hanging particle is $\frac{2 g}{3}$

(iii) Frictional force (on the ring) acts along the forward direction

(iv) Frictional force (on the ring) acts along the backward direction

TestHub · Accepted Answer

String leaves the top of the ring, so a 2 ​ = 2 a 1 ​ Hanging mass m g − T = m a 2 ​ Ring, with friction f forward T + f = m a 1 ​ Torque and rolling ( T − f ) R = m R 2 α , a 1 ​ = R α ⇒ T − f = m a 1 ​ So f = 0, T = ma₁ and a 1 ​ = 3 g ​ , a 2 ​ = 3 2 g ​ Only (i) and (ii) are true Answer: A

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JEE Main 2028 (Class 11)