A solid sphere of mass rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is . The kinetic energy of the sphere at the bottom is

The moments of inertia of two freely rotating bodies and are and respectively. and their angular momenta are equal. If and are their kinetic energies, then

Famous palaeonotologist/Palaeobotanist of India was:

A small object of uniform density roll up a curved surface with an initial velocity . If reaches up to a maximum height of with respect to the initial position. The object is

A uniform rod of length and mass is free to rotate about point . The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about is, the initial angular acceleration of the rod will be

A particle of mass moves in the plane with a velocity along the straight line . If the angular momentum of the particle with respect to origin is when it is at and when it is at , then

Assertion (A): If the system of equations  have non zero solution then 
Reason (R): If the system of equations  has a non zero solution then  is singular

Consider a body, shown in figure, consisting of two identical balls, each of mass connected by a light rigid rod. If an impulse is impared to the body at one of its ends, what would be its angular velocity?

A binary star consists of two stars (mass 2.2 ) and B (mass 11 ), where is the mass of the sun. They are separated by distance and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star about the centre of mass is

A force of- F acts on , the origin of the coordinate system. The torque about the point 1, -(a) is

The area of the region bounded by y=|x-1| and y=1 in sq. units is

For such questions, we should know area of different shapes.

The area of the elliptic quadratic with the semi major axis and semi minor axis as 6 and 4 respectively

For such questions, we should know the formula of area of different shapes.

A solid sphere of radius has moment of inertia about its geometrical axis. If it is melted into a disc of radius and thickness . If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to , then the value of is equal to

The area of the region bounded by y= and the x-axis is

Area of the region bounded by y is

Area of the region bounded by y=and y=2 is