The disc of mass $M$ with uniform surface mass density $\sigma$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $\frac{x}{3} \frac{a}{\pi}, \frac{x}{3} \frac{a}{\pi}$ where $x$ is ....... .

(Round off to the Nearest Integer) $[ a$ is an area as shown in the figure $]$

Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $l$. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega $. If the tensions in the threads are the same during motion, the distance of $M$ from the axis is

Where will be the centre of mass on combining two masses $m$ and $M$ $(M>m)$

For the given uniform square lamina $ABCD$ whose centre is $O$ , pick incorrect statement

Figure shows two cylindrical rods whose center of mass is marked as $A$ and $B$ . Line $AB$ divides the region in two parts one containing point $O$ (region $1$ ) and other containing point $O'$ (region $2$ ). Choose the correct option regarding the center of mass of the combined system.

Two point masses of $0.3\, kg$ and $0.7\, kg$ are fixed at the ends of a rod of length $1.4\, m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of