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

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

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

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

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

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

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

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