Pulley Problem

Q. Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

Q. In the following figure, a body of mass 'm' is tied at one end of a light string and this string is wrapped around the solid cylinder of mass 'M' and radius 'R'. At the moment, t = 0 the system starts moving. If the friction is negligible, angular velocity at time, t would be

1. $\frac{mgRt}{(M+m)}$
2. $\frac{2Mgt}{R(M+2m)}$
3. $\frac{2mgt}{R(M-2m)}$
4. $\frac{2mgt}{R(M+2m)}$

Q. A block of mass 2 kg hangs from the rim of a wheel of radius 0.5 m. On releasing 2 kg from rest the block falls through 5 m height in 2 s. The moment of inertia of the wheel will be

1. $1kg-m^2$
2. $3.2kg-m^2$
3. $2.5kg-m^2$
4. $1.5kg-m^2$