Two bodies of mass 2 kg nd 3 kg are connected to the ends of a string of negligible mass and then passed around a frictionless pulley. Calculate the acceleration of the system.

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.

Two bodies of masses 1 kg and 3 kg respectively are connected rigidly by a vertical spring. The body of mass 3 kg rests on a smooth horizontal surface. The force constant of the spring is 484Nm^(-1) . From the equilibrium position, the mass of 1 kg is displaced vertically through a distance of 0.02 m and then released. calculate (i) and frequency of oscillation of the mass of 1 kg (ii) the maximum velocity of this mass (iii) its oscillation energy and (iv) the reaction of the table on the mass of 3 kg, when mass 1 kg is having harmonic oscillations.

Two bodies of masses m_1 and m_2 are connected byh a ight string passing over a smooth light pulley fixed at the end of an inclined plane.the mass m_1 lies on the inclined plne nd m_2 bags vertically.The system is at rest.Find the angle of the inclination of the inclined plane and the force exerted by the inclined plane on the body of mass m_1 .

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev.//min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?

A spring having with a spring constant 1200 N m^-1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.Determine maximum acceleration of the mass,

A body of mass 0.8 kg is whirled uniformlyt at the end of a string 2 m long.If teh string makes 3 revolutins in 1.5 sec,calculate the tension in the string.

Two masses 5 kg and 3 kg are suspended with the help of massless inextensible strins as shown in the figure. Calculate T_1 and T_2 when whole system is going upwards with acceleration = 2ms^2 (use g=9.8 ms^-2)

A slid object of mass 5 kg floats in a liquid. Calculate the buoyant force acting on the body.

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no slipping.

A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. the acceleration of the mass at the instant when the velocity of the rod is half the terminal velocity.