From a circle of radius $a,$ an isosceles right-angled triangle with the hypotenuse as the diameter of the circle is removed. The distance of the centre of gravity of the remaining portion from the centre of the circle is

$A$ circular plate of diameter '$a$' is kept in contact with a square plate of side '$a$' as shown. The density of the material and the thickness are same everywhere. The centre of mass of the composite system will be ...........

$A$ square plate of side $12 \ cm$ is shown in the figure. If a square of side $2 \ cm$ is cut from one of its corners,where will the center of mass of the remaining part be with respect to the center of the original square? The plate has uniform thickness and density.

$A$ circular hole of radius $R/2$ is cut from a circular disc of mass $M$ and radius $R$ such that the circumference of the hole passes through the center of the disc. What is the moment of inertia of the remaining part about an axis perpendicular to the plane of the disc and passing through its center?

From a uniform circular disc of radius $2 \,cm$ (its centre of mass is at $O$), a circular portion of radius $1 \,cm$ is removed such that the shift in centre of mass is maximum. The disc is now rotated by an angle $\theta$ about an axis perpendicular to its plane and passing through $O$. If the magnitude of displacement of the new centre of mass is $\frac{1}{\sqrt{3}} \,cm$, then the $\theta$ is (in $^{\circ}$)

$A$ spherical hollow is made in a lead sphere of radius $R,$ such that its surface touches the outside surface of the lead sphere and passes through the centre. What is the shift in the centre of mass of the lead sphere due to this?