Two spheres each of mass M and radius R/2 are connected with a mass less rod of length 2R as shown in the-figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod

A disc of mass M and radius R is rolling with angular speed won a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is :–

A sphere S rolls without slipping, moving with a constant speed on a plank P. The friction between the upper surface of P and the sphere is sufficient to prevent slipping, while the lower surface of P is smooth and rests on the ground. Initially, P is fixed to the ground by a pin T. If T is suddenly removed-

An equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction . A horizontal force F is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is-

A uniform rod of mass M and length L lies radially on a disc rotating with angular speed w in a horizontal plane about its axis. The rod does not slip on the disc and the centre of the rod is at a distance R from the centre of the disc. Then the kinetic energy of the rod is-

A uniform rod AB of mass m and length at rest on a smooth horizontal surface. An impulse P is applied to the end B. The time taken by the rod to turn through a right angle is :-

A thin rod of length 4, mass 4m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O & perpendicular to the plane of the paper

A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is not conserved :-

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity v m/s. If it is to climb the inclined surface then v should be:

A rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle ' ' q made by the hinged upper half with the vertical is

A disc of mass M and radius R rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is v, the height to which the disc will rise will be :–

The reaction of with HBr gives

The line parallel to the x-axis and passing through the intersection of the lines  where  is

In this question, we have to find the lines where it lies and what’s its distance from x-axis. If u=ax1+by1+c1=0 and v=ax2+by2+c2=0 are two intersecting lines, then the equation u + kv =0 represents a family of lines. Remember the family of lines

Distance between the two parallel lines and is

When propionic acid is treated with aqueous sodium bicarbonate  is liberated. The ‘C’ of  CO₂ comes from

The following compound is used as