From a solid sphere a small part A is cut by a plane at a distance `R//2` from the centre as shown in figure-4.32. Find the centre of mass of object A.

From a hemisphere of radius R a cone of base radius R/w and height R is cut as shown in figure. Find the height of centre of mass of the remaining object.

The potential at a distance R//2 from the centre of a conducting sphere of radius R will be

A solid sphere of mass m and radius r initially placed at a distance 5r from the centre of a point mass M as shown in figure. Now During displacement, it is also uniformly expanded to a radius 2 r so that its density decreases uniformly throughout its volume. Find the work required in this process.

A cavity of radius R//2 is made inside a solid sphere of radius R . The centre of the cavity is located at a distance R//2 from the centre of the sphere. The gravitational force on a particle of a mass 'm' at a distance R//2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity). [Here g=GM//R^(2) , where M is the mass of the solide sphere]

A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The centre of the smaller circle is at a distance of R/3 from the centre of the larger circle. What is the position of the centre of mass of the plate?

A circular disc of radius (R)/(4) is cut from a uniform circular disc of radius R. The centre of cut portion is at a distance of (R)/(2) from the centre of the disc from which it is removed. Calculate the centre of mass of remaining portion of the disc.