A bullet of mass m leaves the barrel of a gun of mass M with a velocity v. The gun is known to recoil with a velocity V. If k and K respectively denote the kinetic energies of bullet and the gun respectively; then

$K=\left(\frac{m}{M}\right)k$

$K=\left(\frac{m}{M}\right)^2k$

$K=\left(\frac{m}{M}\right)k$

$K=\left(\frac{M}{m}\right)k$

A ball ‘A’ of mass ‘m’ collides with another ball ‘B’ of identical mass at rest. The collision is head on and the coefficient of restitution is e. The ratio of velocities $V_A$ and $V_B$ after collision is

$\left(\frac{1-e}{1+e}\right)$

$\left(\frac{1+e}{1-e}\right)$

$\left(\frac{1-e}{1+e}\right)$

$\left(\frac{1+e^2}{1-e^2}\right)$

$K=\left(\frac{m}{M}\right)k$

$\left(\frac{1-e}{1+e}\right)$

A bullet of mass m leaves the barrel of a gun of mass M with a velocity v. The gun is known to recoil with a velocity V. If k and K respectively denote the kinetic energies of bullet and the gun respectively; then

A net force of 5 N act on a 15 kg object initially at rest. The work done in the third second and the instantaneous power at the end of the third second are

A constant power P is applied to a particle of mass ‘m’ to increase its speed from $v_{1}$ to $v_{2}$ . Assuming the surfaces to be frictionless; the distance traveled by the particle is given by

A ball ‘A’ of mass ‘m’ collides with another ball ‘B’ of identical mass at rest. The collision is head on and the coefficient of restitution is e. The ratio of velocities $V_{A}$ and $V_{B}$ after collision is

A block of mass m moving with a velocity v collides with another block of mass M at rest. The two blocks stick together due to the collision. The loss of K.E. expressed as a fraction of total initial kinetic energy is

A particle with constant total energy E moves in one dimension in a region where the potential energy is represented by U(x). The speed of the particle is zero where.

A body with kinetic energy K moving in +X direction splits up into two parts A and B of equal mass on its own. Part ‘A’ moves back in –X direction with a velocity equal in magnitude to the initial velocity of the body. The kinetic energy of part B will be

An electric motor is used to deliver water through a given pipe at a certain rate (volume per second). To deliver n times water using the same pipe; the power of the motor has to be increased by a factor.

An ideal spring with spring constant $100\, Nm^{-1}$ is suspended from a ceiling. A block of mass 0.1 kg is attached to its free end. The spring is initially unstretched. The mass is released from rest. The maximum extension produced in the spring is

A rubber band stretched through a distance x exerts a restoring force of magnitude $F = a x + b x^{2}$ where a and b are constants. The work done in stretching the unstretched band by L is