Determine the centre of gravity of a thin homogeneous plate having the form of a rectangle with sildes r and `2r` from which a semicircle with a radius r is cut out of figure.

Find the centre of gravity of a thin wire bent to a semicircle of radius r.

Find the centre of mass of a thin, uniform disc of radius R from which a small concentric disc of radius r is cut.

Find the dimensions of the rectangle of maximum area that can be inscribed in a semicircle of radius r.

Rectangles are inscribed inside a semicircle of radius r. Find the rectangle with maximum area.

A thin homogeneous lamina is in the form of a circular disc of radius R. From it a circular hole exactly hall the radius of the lamina and touching the lamina's circumference is cut off. Find the centre of mass of the remaining part.

semicircle of radius R. The electric field at the centre is -

Let x and y be the length and bredth of the rectangle ABCD in a circle having radius r. Let angleCAB=theta (Ref. Figure). If triangle represent area of the rectangle and r is a constant. Show that the rectangle of maximum area that can be inscribed in a circle of radius r is a square of side sqrt2r .

In the figure shown, find out centre of mass of a system of a uniform circular plate of radius 3R from O in which a hole of radius R is cut whose centre is at 2R distance from the centre of large circular plate

In the figure shown, find out centre of mass of a system of a uniform circular plate of radius 3R from O in which a hole of radius R is cut whose centre is at 2R distance from the centre of large circular plate