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

Two particles of mass $5\, kg$ and $10\, kg$ respectively are attached to the two ends of a rigid rod of length $1\, m$ with negligible mass. The centre of mass of the system from the $5\, kg$ particle is nearly at a distance of $..........\, cm$

Obtain the position of centre of mass of a thin rod of uniform density.

A uniform square plate abcd has a mass of $1 \,kg$. If two point masses each of $20 \,g$ are placed at the corners $b$ and $c$ as shown, then the centre of mass shifts on the line

The $(x -y)$ co-ordinates $(in\ cm)$ of the centre of mass of letter $E$ relative to the origin $O$ , whose dimensions are shown in the figure is :
(Take width of the letter $2\ cm$ every where) :

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\frac{\alpha}{R}$ form the centre of the bigger disc. The value of a is $\alpha $ is