Consider a cylindrical tank of radius $$1 \mathrm{~m}$$ is filled with water. The top surface of water is at $$15 \mathrm{~m}$$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $$5 \mathrm{~m}$$ from the bottom. A force of $$5 \times 10^{5} \mathrm{~N}$$ is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure $$\mathrm{P}_{\mathrm{A}}=1.01 \times 10^{5} \mathrm{~Pa}$$, density of water $$\rho_{\mathrm{W}}=1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and gravitational acceleration $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

A vessel contains $$14 \mathrm{~g}$$ of nitrogen gas at a temperature of $$27^{\circ} \mathrm{C}$$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :

Take $$\mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$$.

A slab of dielectric constant $$\mathrm{K}$$ has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $$\frac{3}{4} \mathrm{~d}$$, where $$\mathrm{d}$$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :

(Given $$\mathrm{C}_{0}$$ = capacitance of capacitor with air as medium between plates.)

A uniform electric field $$\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}$$ is created between two parallel plates of length $$1 \mathrm{~m}$$ as shown in figure, (where $$\mathrm{m}=$$ mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The angle of the deviation $$(\theta)$$ of the path of the electron as it comes out of the field will be _________.