Two spherical bodies of mass $$M$$ and $$5M$$ & radii $$R$$ & $$2R$$ respectively are released in free space with initial separation between their centers equal to $$12R$$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius $$4$$ $$R$$ is made from an iron plate of thickness $${t \over 4}.$$ Then the relation between the moment of inertia $${I_X}$$ and $${I_Y}$$ is

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $${C_p}/{C_V}$$ for the gas is

The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in the time period of the pendulum of increased length is