A photoelectric surface is illuminated successively by monochromatic light of wavelengths $$\lambda $$ and $${\lambda \over 2}.$$ If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

A bottle has an opening of radius a and length b. A cork of length b and radius (a + $$\Delta $$a) where ($$\Delta $$a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is $$\mu $$ then the force needed to push the cork into the bottle is :

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as
B = B₀e$${^{{{ - t} \over r}}}$$ , where B₀ and $$\tau $$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time (t $$ \to $$ $$\infty $$) is :

Within a spherical charge distribution of charge density $$\rho $$(r), N equipotential surfaces of potential V₀, V₀ + $$\Delta $$V, V₀ + 2$$\Delta $$V, .......... V₀ + N$$\Delta $$V ($$\Delta $$ V > 0), are drawn and have increasing radii r₀, r₁, r₂,..........r_N, respectively. If the difference in the radii of the surfaces is constant for all values of V₀ and $$\Delta $$V then :