Centre of Mass Frame

Calculate the maximum extension of the spring of spring constant $k=200 \mathrm{N} {\mathrm{m}}^{-1}$, initially the spring is unstretched, when the two blocks of mass $3 \mathrm{kg}$ and $6 \mathrm{kg}$ respectively are placed on a smooth horizontal surface, and they are given velocities as shown in the figure

A plank is moving in a horizontal direction with a constant acceleration $a\hat{\mathrm{i}}$. A uniform rough cubical block of side $l$ rests on the plank and is at rest relative to the plank.

Let the centre of mass of the block be at $\left(0, \frac{l}{2}\right)$ at a given instant. If $a=\frac{g}{10}$, then the normal reaction exerted by the plank on the block at that instant acts at

Consider a two block system having masses $M_A=3 \mathrm{kg}$ and $M_B=2 \mathrm{kg}$, as shown in the figure. If block A is pushed towards the centre of mass through a distance $200 \mathrm{cm}$, by what distance should the block $B$ be moved so as to keep the centre of mass at the same position.

A uniform semi-ring of radius $\mathrm{\pi }$ meter is rotating about one of its corners on a frictionless horizontal table. The plane of motion is the same as that of the semi-ring. The hinge (origin) is suddenly removed. Find the co-ordinates (in $\mathrm{m}$) of point $B$ $10 \mathrm{s}$ after removing the hinge.

A body of mass $m$ moving with a velocity $v$ is approaching a second body of same mass but at rest. The total kinetic energy of the two bodies with respect to centre of mass frame is:

A stationary pulley carries a rope one end of which supports a ladder with a man and the other a counterweight of mass $M$ . The man of mass $m$ climbs up a distance $l$ with respect to the ladder and then stops. The displacement of the centre of mass of this system is

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 the plank is $3M$, the distance that the man moves relative to the ground is

A man weighing  $80 \mathrm{kg}$ is standing in a trolley weighing  $320 \mathrm{kg}$. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$, then after $4 \mathrm{s}$, his displacement relative to the ground will be

Two particles of masses $m$ and $2m$ are connected by a string of length $L$ and placed at rest over a smooth horizontal surface. The particles are then given velocities as indicated in the figure shown. The tension developed in the string will be

A thick straight wire of length$\mathrm{\pi } \mathrm{m}$ is fixed at its midpoint and then bent in the form of a circle. The shift in its center of mass is

Two blocks $A$ and $B$ of masses $m$ and $2m$ respectively are attached at opposite ends of a spring of constant $K$ and is placed on a smooth horizontal surface. Spring is initially at its natural length $l$. $A$ is given a velocity $2V_0$ and $B$ given velocity $V_0$ as shown.


Maximum separation between $m$ and centre of mass of the system will be:

A rod of mass m and length $l$ is placed vertically on a horizontal smooth surface. A small disturbance is given at lowest end in horizontal direction. The locus of a point P which is at a distance r on the rod from lowest point of the rod will be a/an