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

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…

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…

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…

A mass 3 m , initially at rest at the origin explodes into three fragments of equal mass. Two of the fragments have speed $v$ each and move perpendicular to each other. The third fragment will move with a speed

The bob $A$ of a simple pendulum is released when the string makes an angle of $45^{\circ}$ with the vertical. It hits an other bob $B$ of the same material and same mass kept at rest on the table. If the collision is…

Two point masses 1 and 2 move with uniform velocities $\mathbf{v}_1$ and $\mathbf{v}_2$ respectively. Their initial position vectors are $\mathbf{r}_1$ and $\mathbf{r}_2$, respectively. Which of the following should be…

A mass $3 m$, initially at rest at the origin explodes into three fragments of equal mass. Two of the fragments have speed $v$ each and move perpendicular to each other. The third fragment will move with a speed

Nucleus of mass number $A$, originally at rest, emits the $\alpha$-particle with speed $v$. The daughter nucleus recoils with a speed of

A ball is projected from the point $O$ with velocity $20 \mathrm{~m} / \mathrm{s}$ at an angle of $60^{\circ}$ with horizontal as shown in the figure. At highest point of its trajectory, it strikes a smooth plane of…

A bullet of mass 10 g is fired from a gun of mass 1 kg . If the recoil velocity is $5 \mathrm{~m} / \mathrm{s}$, the velocity of the muzzle is