Center of Mass Momentum and Collision

A composite system of two uniform rods of same metal are shown in the figure. Lengths of rods are as shown in figure. The co-ordinates of the centre of mass of the system of rods are

A gas molecule of mass $m$, moving with velocity $\vec{v} = a\hat{i} + b\hat{j} + c\hat{k}$ hits a container wall that is parallel to the $xz$-plane. Assuming a perfectly elastic collision, what is the change in…

Two billiard balls A and B, each of mass $50\ \text{g}$ and moving in opposite directions at a speed of $5\ \text{m/s}$ each, collide and rebound at a same speed. The magnitude of impulse imparted to each ball is

A particle 'A' of mass ' 2m' and having initial velocity $'u_A'$ collides with particle B of mass ' m / 2' at rest. The collision is head on and elastic. If $\lambda_A$ and $\lambda_B$ are the de-Broglie wavelength of…

On a friction-less surface, a block of mass M moving at speed $v$ collides elastically with another block (of mass M) initially at rest. After collision, the first block moves at an angle $\theta$ to its initial…

The force $'F'$ acting on a particle of mass $'m'$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8s$ is:

Point masses $m_{1}$ and $m_{2}$ are placed at the opposite ends of rigid rod of length $\text{L}$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $\text{L}$…

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R), Assertion (A): When a fire cracker (rocket) explodes in mid air, its fragments fly in such a way that they…

A moving block having mass $m,$ collides with another stationary block having mass $4m.$ The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v,$ then the value of…

The centre of mass of a homogenous semi-circular plate of radius $\mathrm{r}$ is located at $\mathrm{A}$ as shown in the figure. The distance OA is

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2 R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the…

Two particles of masses in the ratio $1: 2$ are placed along a vertical line. The lighter particle is raised through a height of $9 \mathrm{~cm}$. To raise the centre of mass of the system by 2 $\mathrm{cm}$, the…