Question

A light string is wrapped on a cylindrical shell and a fraction of length of string is unwrapped. A particle of mass 2M is attached on another end of string as shown. The system is kept in a vertical plane and cylinder can freely rotate about the axis of cylinder. Particle is released as shown in figure. Assuming there is no slipping between cylinder and string. Choose the correct option(s).

• A. The acceleration of the particle is 2g/3.
• B. The tension in the string is 2Mg/3.
• C. The angular acceleration of the cylinder is 2g/(3R).
• D. The acceleration of the center of mass of the system is 4g/9.

Answer 1

Answer: (A), (B), (C), (D)

Multiple Correct Options

Answer 2

Apply Newton's second law to the particle and the cylindrical shell. Use the torque equation for the cylindrical shell. Relate the linear acceleration of the particle to the angular acceleration of the shell using the no-slipping condition. Solve the resulting system of equations to find the acceleration of the particle and the tension in the string. Calculate the angular acceleration of the cylinder and the acceleration of the center of mass of the system. The correct options are the statements that match these calculated values.

Answer: Since the options are not provided, we cannot select specific option numbers. However, the correct options are statements that match the calculated values: acceleration of the particle $a = 2g/3$, tension in the string $T = 2Mg/3$, angular acceleration of the cylinder $\alpha = 2g/(3R)$, and acceleration of the center of mass of the system $A_{CM} = 4g/9$.