Centre of Mass

A ball of mass $3\mathrm{kg}$ and a ball of mass $2\mathrm{kg}$ roll towards each other on a flat surface. How for is the centre of mass from the $3\mathrm{kg}$ ball of the $2$ balls are separated by $6\mathrm{m}$?

Two particles of masses $2\mathrm{kg}$ and $3\mathrm{kg}$ are at rest and are separated by $10\mathrm{m}$. If they move towards each other under the mutual force of attraction, they would meet at ________.

Masses $1\mathrm{kg}, 1.5\mathrm{kg}, 2\mathrm{kg} \mathrm{and} "\mathrm{M}"\mathrm{kg}$ are situated at $\left(2, 1, 1\right)$ and $\left(1, 2, 1\right)$, $\left(2, -2, 1\right)$ and $\left(-1, 4, 3\right)$. What is the value of $"\mathrm{M}"$ if their centre of mass is at $\left(1, 1, \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$?

From a uniform disc of radius $\mathrm{R}$, a circular section of radius $\raisebox{1ex}{$\mathrm{R}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ is cut out. The centre of mass hole is at $\raisebox{1ex}{$\mathrm{R}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ from the centre of the original disc. Locate the centre of gravity of the resulting flat body.

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 $\text{α}R$ from the centre of the bigger disc. The value of $\text{α}$ is

A rigid body can be ____________.

A _____ rod is an example of rigid body.

Is the human body a rigid body?

What is called a rigid body?

The center of mass of a system of particles does not depend upon force acting on particle.

Define a rigid body.

Give an example to show that the following statement is false. 'Any two forces acting on a body can be combined into single force that would have same effect'.

The $y–$ coordinate of centre of mass of a thin and uniform semicircular ring of radius $r$ shown in figure is

Centre of mass of a uniform ring is at the _____ of the ring.
(Choose from: circumference/centre)

In case of an isolated system, the centre of mass of the system moves with a constant _____.

Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

Which of the following points is the likely position of the centre of mass of the system shown in figure?

Two particles each of mass $1 \mathrm{g}$ are placed at a distance of $1 \mathrm{m}$ and $3 \mathrm{m}$ respectively from the origin along $\mathrm{X}$-axis. The centre of the mass of the system of the particles is

Two particles each of mass $1 \mathrm{g}$ are placed at a distance of $1 \mathrm{m}$ and $3 \mathrm{m}$ respectively from the origin along $x$-axis. The centre of the mass of the system of the particles is

Centre of mass of a uniform ring is at the _____ of the ring.