The centre of mass of a solid hemisphere of radius $8 \, cm$ is $X \, cm$ from the centre of the flat surface. Then the value of $X$ is $......$

$A$ circular disc of radius $R$ has a uniform thickness. $A$ circular hole of diameter equal to the radius of the disc has been cut out as shown. The distance of the centre of mass of the remaining disc from point $O$ is

$A$ spherical cavity of radius $r$ is carved out of a uniform solid sphere of radius $R$ as shown in the figure below. The distance of the centre of mass of the resulting body from that of the solid sphere is given by

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 disc of radius $R$ is removed from one end of a bigger circular disc of radius $2R$. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

$A$ uniform thin metal plate of mass $10 \ kg$ with the dimensions shown in the figure is given. The ratio of the $x$ and $y$ coordinates of the center of mass of the plate is $\frac{n}{9}$. The value of $n$ is: