Centre of Mass and Its Motion

If the resultant of all the external forces acting on a body be zero, the centre of mass of the system

Two bodies of different masses $2 \mathrm{kg}$ and $4 \mathrm{kg}$ are moving with velocities $2 \mathrm{m} {\mathrm{s}}^{-1}$ and $1 \mathrm{m} {\mathrm{s}}^{-1}$ towards each other due to mutual gravitational attraction. Then the velocity of the centre of mass is

If the separation between carbon and oxygen in $\mathrm{CO}$ molecule is $0.12 \mathrm{nm}$, then the distance of the center of mass from the carbon atom is

A block of mass $m$ is projected towards a wedge of mass $M$ with a velocity $u$ as shown in the figure below. All the surfaces are smooth. Find the expression for the maximum height attained by the block as it moves on the surface of the wedge.

Two masses at a distance equal to $D$ are moving towards each other due to gravitational pull as shown in the figure below. Find the expression for the relative velocity of two masses when the distance between the two masses become $D/2$.

The concept of reduced mass can be used in the problems where the force between the two masses is:

Two masses $m$ and $2m$ are connected by a spring are kept on a frictionless table as shown in the figure below. The block of mass $m$ is imparted the velocity equal to $v$ towards right. Find the maximum compression in the spring.

What do you understand by reduced mass?

A uniform thin wooden plank $AB$ of length $L$ and mass $M$ is kept on a table with its $B$ end slightly outside the edge of the table. When an impulse $J$ is given to the end $B$, the plank moves up with centre of mass rising a distance $h$ from the surface of the table. Then,

A small ring is rolling without slipping on the circumference of a large bowl as shown below in the figure. The ring is moving down at $P_1$, comes down to the lower most point $P_2$ and is climbing up at $P_3$. Let ${\overrightarrow{v}}_{CM}$ denote the velocity of the centre of mass of the ring. Choose the correct statement regarding the frictional force on the ring.

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1 \stackrel{\circ }{\mathrm{A}}$. Given, mass of carbon atom is 12 a.m. $u$ and mass of oxygen atom is 16 a.m.u. Calculate the position of the centre of mass of the carbon monoxide molecule.

A tank with uniform cross-sectional area $A$ is filled with a liquid of density $\rho$ upto a height $h.$ What is the potential energy stored in the system ?  (where $g$ denotes the acceleration due to gravity)

The distance of the centre of mass of the $T-$shaped plate from $O$ is,

Two particles of equal mass have velocities ${\overrightarrow{v}}_1=2\hat{i} \mathrm{m} {\mathrm{s}}^{-1}$ and ${\overrightarrow{v}}_2=2\hat{j} \mathrm{m} {\mathrm{s}}^{-1}$. First particle has an acceleration ${\overrightarrow{a}}_1=(3\hat{i}+3\hat{j}) \mathrm{m} {\mathrm{s}}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

A man of mass $M$ stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of plank is $\frac{M}{3}$, the distance that the Man moves relative to the ground is:

A circular hole of radius $1 \mathrm{cm}$ is cut off from a disc of radius $6 \mathrm{cm}$. The centre of the hole is $3 \mathrm{cm}$ from the centre of the disc. Then the distance of the centre of mass of the remaining disc from the centre of the disc is

For a bangle, the centre of mass lie outside the body.

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

Two particles A and B initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of A is $v$ and speed of B is $2v$, the centre of mass (CM) remains at rest. This statement is _____. Choose from (True/False).