$A$ man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as

$A$ bullet of $10\, \text{g}$, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100\, \text{m/s}$. The length of the pendulum is $0.5\, \text{m}$ and the mass of the bob is $1\, \text{kg}$. The minimum value of $v$ in $\text{m/s}$ so that the pendulum completes a vertical circle is: (Assume the string to be inextensible and $g=10\, \text{m/s}^2$)

Two blocks $A(5 \ kg)$ and $B(2 \ kg)$ attached to the ends of a spring of spring constant $k = 1120 \ N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously,velocities of $3 \ m/s$ and $10 \ m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$. Then:

$A$ body of mass $500 \ g$ is falling from rest from a height of $3.2 \ m$ from the ground. If the body reaches the ground with a velocity of $6 \ ms^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $J$)

$A$ block of mass $1 \ kg$ is moved by a distance of $1 \ m$ on a horizontal surface by applying a force of $8 \ N$. Then it is lifted to a height of $2 \ m$. The total work done is ... $J$. (Take $g = 10 \ m/s^2$)

Two bodies of different masses $m_1$ and $m_2$ have equal momenta. Their kinetic energies $E_1$ and $E_2$ are in the ratio: