From the homogeneous square plate we cut a triangle (Figure). Side of the square is $a$ and. the apex of the triangle is at the center of the square. Distance fiom the center of the square to the center of mass of the remainder of the plate is

The identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is_____

A system consists of $3$  particles each of mass $m$ and located at $(1, 1), (2, 2), (3, 3)$. The co-ordinate of the centre of mass are

Write the difference between centre of gravity and centre of mass of a body?

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

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