$A$ circular portion of radius $R_2$ has been removed from one edge of a circular disc of radius $R_1$. The correct expression for the centre of mass for the remaining portion of the disc 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 ...........

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

$A$ semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in the figure. The distance of the centre of mass $C$ of the remaining plate from point $O$ is:

The position of the centre of mass of the uniform plate as shown in the figure is

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 $^{\circ}$)