The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of sound in helium $$(He)$$ at the same temperature will be (assume both gases to be ideal)

A spherical solid ball of volume $$V$$ is made of a material of density $${\rho _1}$$. It is falling through a liquid of density $${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $$v,$$ i.e., $${F_{viscous}} = - k{v^2}\left( {k > 0} \right).$$ The terminal speed of the ball is

A planet in a distant solar system is $$10$$ times more massive than the earth and its radius is $$10$$ times smaller. Given that the escape velocity from the earth is $$11\,\,km\,{s^{ - 1}},$$ the escape velocity from the surface of the planet would be

Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is