Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of Earth is

If two bodies of masses 2 kg and 3 kg are moving at right angles with velocities $20 \mathrm{~ms}^{-1}$ and $10 \mathrm{~ms}^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is

The kinetic energy of a particle executing simple harmonic motion at a displacement of 3 cm from the mean position is 4 mJ . If the amplitude of the particle is 5 cm , then the maximum force acting on the particle is

A body of mass 1 kg is attached to the lower end of a vertically suspended spring of force constant $600 \mathrm{~N}-\mathrm{m}^{-1}$. If another body of mass 0.5 kg moving vertically upward hits the suspended body with a velocity $3 \mathrm{~ms}^{-1}$ and embedded in it, then the frequency of the oscillation is