Laws of Motion ...

The tension in the string in the pulley system shown in the figure is

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is 2 x 109 Nm^-2. What should be the minimum radius of the wire used if it is not to break? (take, g =10 ms^-2)

Two masses A and B of 15 kg and 10 kg are connected with a string passing over a frictionless pulley fixed at the corner of a table (as shown in figure). The coefficient of friction between the table and block is 0.4. The minimum mass of C, that may be placed on A to prevent it from moving is

Two masses m₁and m₂ (m₁ > m₂) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ . The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁ = mg (sin θ – μ cos θ) to P₂ = mg (sin θ + μ cos θ), the frictional force f versus P graph will look like

A block of mass 200 kg is being pulled up by men on an inclined plane at angle of 45° as shown in the figure. The coefficient of static friction is 0.5. Each man can only apply a maximum force of 500 N. Calculate the number of men required for the block to just start moving up the plane.

Two blocks of equal masses m are released from the top of a smooth fixed wedge as shown in the figure. The acceleration of the centre of mass of the two blocks is

A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A block is kept on an inclined plane of inclination θ and length l. The velocity of particle at the bottom of incline is (the coefficient of friction is µ)

A block of mass M is pulled along horizontal frictionless surface by a rope of mass m. Force P is applied at one end of rope. The force which the rope exerts on the block is