Question

A cube of mass M starts at rest from point 1 at a height 4R, where R is the radius of the circular track. The cube slides down the frictionless track and around the loop. Find the force which the track exerts on the cube at point 2.

A body tied to one end of a string is made to revolve in a vertical plane. Derive the expression for the velocity of the body and tension in the string at any point. Hence find (i) tension at the bottom and top of the circle. (ii) Minimum velocity at the lowest point so that it is just able to loop the vertical loop and (c) the minimum velocity at the top.

What is the acceleration of the block and trolley system shown in a figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, what is the tension in the string? (Neglect the mass of the string.) (take g = 10 ms^-2).

Consider two masses m1 and m2 connected by a light and inextensible string passing over a smooth light pulley which is fixed by a rigid cord, from a rigid support as shown in figure. This device is also known as Atwood's machine. Find the tension in the rope and acceleration of each block.