A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

If two soap bubbles of different radii are connected by a tube

Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retarding viscous force acting on the spherical ball is

According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right)^n},$$ where $${\Delta \theta }$$ is the difference of the temperature of the body and the surrounding, and $$n$$ is equal to :