$A$ man weighing $80\, kg$ is standing at the centre of a flat boat and he is $20\, m$ from the shore. He walks $8\, m$ on the boat towards the shore and then halts. The boat weight $200\, kg$. ........ $m$ far is he from the shore at the end of this time.

As shown in figure, when a spherical cavity (centred at $\mathrm{O})$ of radius $1$ is cut out of a uniform sphere of radius $\mathrm{R} \text { (centred at } \mathrm{C}),$ the centre of mass of remaining (shaded) part of sphere is at $G$, i.e, on the surface of the cavity. $\mathrm{R}$ can be detemined by the equation

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 centre of mass of a body

A rod of length $3\, m$ and its mass per unit length is directly proportional to the distance $x$ from its one end. The center of gravity of the rod from that end will be at ........ $ m$

From a circular disc of radius $R$ a triangular portion is cut (see fig.). The distance of  $COM$ of the remaining disc from centre of disc $O$ is:-