Centre of Mass

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

Four particle of mass$5,3,2,4 \mathrm{kg}$are at the points $(1,6),(-1,5),(2,-3),(-1,-4)$Find the coordinates of their centre of mass.

The Coordinates of centre of mass of the following system are

Two particles of mass $1 \mathrm{kg}$and $2 \mathrm{kg}$ are located at $\mathrm{x} = 0$ and $\mathrm{x} = 3 \mathrm{m}$. Find the position of their centre of mass.

Find out the centre of mass of an isosceles triangle of base length $\mathrm{a}$ and altitude $\mathrm{b}.$ Assume that the mass of the triangle is uniformly distributed over its area.

What is the rolling motion

Define rotational motion and mention its conditions.

Define translatory motion and state its condition.

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

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).

Centre of mass of rectangular lamina lies on the point of intersection of the _____.

The centre of mass of a body lies always inside the body.

Two blocks of masses $8 \mathrm{kg}$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $12 \mathrm{m} {\mathrm{s}}^{-1}$ to the block in the direction of other block. The velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the centre of mass is:-

For which of the following does the centre of mass lie outside the body ?

In the figure shown the system is at rest initially. Two persons $A$ and $B$ of masses $40 \mathrm{kg}$ each move with speeds $v_1$ and $v_2$ respectively towards each other on a plank lying on a smooth horizontal surface as shown in the figure. Plank travels a distance of $20 \mathrm{m}$ towards right direction in $5 \sec .$ (Here $v_1$ and $v_2$ are given with respect to the plank). Then:

(i) $v_1=10 \mathrm{m} {\mathrm{s}}^{-1}, {\mathrm{v}}_2=0 \mathrm{m} {\mathrm{s}}^{-1}$
(ii)$v_1=15 \mathrm{m} {\mathrm{s}}^{-1}, {\mathrm{v}}_2=5 \mathrm{m} {\mathrm{s}}^{-1}$
(iii)$v_1=20 \mathrm{m} {\mathrm{s}}^{-1}, {\mathrm{v}}_2=10 \mathrm{m} {\mathrm{s}}^{-1}$

On a horizontal frictionless frozen lake, a girl $(36 \mathrm{kg})$ and a box $(9 \mathrm{kg})$ are connected to each other by means of a rope. Initially, they are $20 \mathrm{m}$ apart. The girl exerts a horizontal force on the box pulling it towards her. How far has the girl travelled when she meets the box?