Three identical spheres A, B, and C are placed on a smooth horizontal table such that their centers form an equilateral triangle. Sphere A is given a velocity $v$ towards B. After colliding elastically with B, A comes to rest. What is the speed of C after all collisions have ceased?

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

An engine develops 10 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m $\left( {g = 10\;m/se{c^2}} \right)$

Two identical objects collide elastically in one dimension. Object 1 has an initial velocity of $3\ m/s$, and Object 2 is initially at rest. What is the velocity of Object 2 after the collision?

It is observed that the force required to tow a boat at constant velocity is proportional to the velocity. It takes 16 HP to tow a boat at a velocity of $2{\rm{\;km}}{{\rm{h}}^{ - 1}}$. The horse power required to tow this boat at a velocity of $3{\rm{\;km}}{{\rm{h}}^{ - 1}}$ is

An $\alpha$-particle of mass m suffers one dimensional elastic collision with a nucleus of unknown mass. After the collision the $\alpha$-particle is scattered directly backward losing 75% of its kinetic energy .then the mass of the nucleus is

If two particles A and B are moving with constant velocities and their relative position vector $\overrightarrow{r_{BA}}$ is not parallel to their relative velocity $\overrightarrow{v_{BA}}$, what can be concluded about their collision?

A marble going at a speed of $2\,\,m/s$ hits another marble of equal mass at rest. If the collision is perfectly elastic, then the velocity of the first marble after collision is $\left( {in\,\,m/s} \right)$

Two boats are moving with constant velocities. Boat A starts at position $\overrightarrow{r_A} = 10\hat{i} + 5\hat{j}$ with velocity $\overrightarrow{v_A} = 2\hat{i} + \hat{j}$. Boat B starts at $\overrightarrow{r_B} = 2\hat{i} + 15\hat{j}$ with velocity $\overrightarrow{v_B} = 3\hat{i} - 2\hat{j}$. Find the time at which they will collide, if they do.

A neutron of mass $m$ collides elastically with a stationary nucleus of mass $4m$. After the collision, the neutron is deflected through $90^\circ$. What fraction of its initial kinetic energy does the neutron lose in the collision?

An engine pump is used to pump a liquid of density $\rho$ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is