Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?

Where does the centre of mass of a uniform triangular lamina lie?

Can centre of mass of a body coincide.with the geometrical centre of the body always?

Is centre of mass same as the centre of gravity of a body? How can a rigid body be balanced?

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is: (i)T,(II) T-(mv^2)//l, (iii) T+(MV^2)/l, (iv)0

Given the M.I. of a dise of mass M and radius R about any of its diameter to be MR^2 /4. Find its M.I about an axis (i) passing through its centre and normal to it, and (ii) passing through a point at its edge and normal to it.

Three bodies - a ring, a solid cylinder and a solid sphere of same mass and radii roll down an inclined plane from the same height. Which of the three will reach the ground first?