Work done in increasing the size of a soap bubble from a radius of $$3$$ $$cm$$ to $$5$$ $$cm$$ is nearly (Surface tension of soap solution $$ = 0.03N{m^{ - 1}},$$

Two bodies of masses $$m$$ and $$4$$ $$m$$ are placed at a distance $$r.$$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:

A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where $$t$$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $$10kg$$-$${m^2}$$ the number of rotation made by the pulley before its direction of motion is reversed, is:

A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m$$ and radius $$R.$$ Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $$m,$$ if the string does not slip on the pulley, is: