A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t₁ it is found that the electric field is zero at a spatial point z₁. The next zero that occurs in its neighbourhood is at z₂. The frequency of the electroagnetic wave is :

A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle $$\alpha $$ with the horizontal, will be proportional to : (see figure)

A solid ball of radius R has a charge density $$\rho $$
given by $$\rho $$ = $$\rho $$_o (1 $$-$$ $${\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}$$) for 0 $$ \le $$ r $$ \le $$ R. The electric field outside the ball is :