Centre of Mass and Its Motion

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragment with equal masses fly in mutually perpendicular directions with speeds of 21 ms^-1​. The velocity of heaviest fragment in ms^-1 will be

The mass of two objects $A$ and $B$ are $100 \mathrm{g}$ and $300 \mathrm{g}$ respectively. Their velocities are $\overrightarrow{v_{\mathrm{A}}}=\left(\hat{\mathrm{i}}+7\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and $\overrightarrow{v_B}=\left(\hat{\mathrm{j}}-6\hat{\mathrm{i}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. What will be the velocity of centre of mass in $\mathrm{m} {\mathrm{s}}^{-1}$?

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

The $K.E.$ of a body is doubled. Its momentum will

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.

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)

A bullet of mass $\mathrm{10\; g}$ moving horizontally with a velocity of $400 \mathrm{m }{\mathrm{s}}^{-1}$ strikes a wooden block of mass $\mathrm{2\; kg}$ which is suspended by a light inextensible string of length $\mathrm{5\; m.}$ As a result, the centre of gravity of the block is found to rise a vertical distance of $\mathrm{10\; cm.}$ The speed of the bullet after it emerges out horizontally from the block will be

In the non-relativistic regime, if the momentum, is increased by $100\%,$ the percentage increase in kinetic energy is

Internal forces can change

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

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 ?