A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\% $$. What is the fundamental frequency of steel if density and elasticity of steel are $$7.7 \times {10^3}\,kg/{m^3}$$ and $$2.2 \times {10^{11}}\,N/{m^2}$$ respectively ?

A charge $$Q$$ is uniformly distributed over a long rod $$AB$$ of length $$L$$ as shown in the figure. The electric potential at the point $$O$$ lying at distance $$L$$ from the end $$A$$ is

The above $$p$$-$$v$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $$T,$$ density of liquid is $$\rho $$ and $$L$$ is its latent heat of vaporization.