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 $......$

$A$ uniform square plate has a side of length $2R$. $A$ circular piece of maximum possible area is cut and removed from one of the quadrants of the plate as shown in the figure. Calculate the shift in the centre of mass of the plate.

The sector of a circular plate shown in the figure has its center of mass at $y_{CM} =$

$A$ 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

The coordinates of the centre of mass of a uniform $L$-shaped plate of mass $3 \ kg$ shown in the figure is:

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The center of the hole is at $(a/4, a/4)$ from the center of the square. The distance of the center of mass of the resulting plate from the center of the square is: