Physics

Power $=$ Number of photons emitted per sec $*$  Energy of 1 photon

$\mathrm{P}=\mathrm{n}*\frac{\mathrm{h}\mathrm{c}}{\lambda }\Rightarrow \mathrm{n}\propto \lambda$

$K=\frac{\left(\frac{Q}{r}\right)\mathrm{\Delta }x}{\mathrm{\Delta }AT}$

$\begin{array}{ll}\Rightarrow & \frac{\left({\mathrm{M}\mathrm{L}}^2{\mathrm{T}}^{-2}\right)\left(\mathrm{L}\right)}{\left({\mathrm{L}}^2\right)\left(\theta \right)\left(\mathrm{T}\right)}\\ \Rightarrow \mathrm{}& {\mathrm{M}}^1{\mathrm{L}}^{1-}{\mathrm{T}}^{-3}{\theta }^{-1}\end{array}$

Multimeter will show deflection when current will flow to charge the capacitor.

$\begin{array}{rr}& \Rightarrow \mathrm{}{V}^2=U^2+2gS\\ & \Rightarrow \mathrm{}{V}^2=0+2g(h-y)\\ & \Rightarrow \mathrm{}{V}^2=2gh-2gy\\ & \Rightarrow \mathrm{}V=\sqrt[]{2gh-2gy}\end{array}$

Heat lost by steam $=$  Heat gained by water and calorimeter.

$\begin{array}{rr}& \mathrm{m}*540+\mathrm{m}*1*(100-31)=200\\ & 540\mathrm{m}+69\mathrm{m}=1200\\ & \mathrm{m}=\frac{1200}{609}\approx 2\end{array}$

Solar constant $=\frac{\text{Energy}}{\text{Area}*\text{Time}}=\frac{{\mathrm{M}\mathrm{L}}^2{\mathrm{T}}^{-2}}{{\mathrm{L}}^2*\mathrm{T}}={\mathrm{M}\mathrm{L}}^{?}{\mathrm{T}}^{-3}$

Torque of centrifugal force about $A$

$=\int d=\int \left[dm{\omega }^2(x\mathrm{s}\mathrm{i}\mathrm{n}?\theta )\right](x\mathrm{c}\mathrm{o}\mathrm{s}?\theta )$

$={\int }_0^{\mathcal{l}}?\frac{\mathrm{m}}{\mathcal{l}}\mathrm{d}x{\omega }^2{x}^2\mathrm{s}\mathrm{i}\mathrm{n}?\theta \mathrm{c}\mathrm{o}\mathrm{s}?\theta$

$=\frac{m}{\mathcal{l}}{\omega }^2\mathrm{s}\mathrm{i}\mathrm{n}?\theta \mathrm{c}\mathrm{o}\mathrm{s}?\theta {\left[\frac{x^3}{3}\right]}_0^{\mathcal{l}}=\frac{m{\omega }^2{\mathcal{l}}^2\mathrm{s}\mathrm{i}\mathrm{n}?\theta \mathrm{c}\mathrm{o}\mathrm{s}?\theta }{3}$

  ${\tau }_{\mathrm{m}\mathrm{g}}={\tau }_{\text{centrifugal}}$ (about A)

$\mathrm{m}\mathrm{g}\frac{\mathcal{l}}{2}\mathrm{s}\mathrm{i}\mathrm{n}?\theta =\frac{m{\omega }^2{\mathcal{l}}^2\mathrm{s}\mathrm{i}\mathrm{n}?\theta \mathrm{c}\mathrm{o}\mathrm{s}?\theta }{3}$

$\mathrm{c}\mathrm{o}\mathrm{s}?\theta =\frac{3g}{2\mathcal{l}{\omega }^2}$

$eVs=hv-?$

$\begin{array}{rr}& \text{At}{\mathrm{V}}_{\mathrm{s}}=0\Rightarrow \mathrm{h}\mathrm{v}=?\\ & \Rightarrow \mathrm{}?=\left. [6.62*{10}^{-34}\right]\left. [{10}^{14}\right]\left[5.5\right]\\ & \Rightarrow \mathrm{}?=\frac{\left. [6.62*{10}^{-34}\right]\left. [{10}^{14}\right]\left[5.5\right]\mathrm{e}\mathrm{V}}{\left(1.6*{10}^{-19}\right]}\end{array}$

$=2.27$

$g=\frac{Ax}{{\left(x^2+a^2\right)}^{3/2}}$  $\frac{}{{\left({}^{}{}^{}\right)}^{}}$

$\Rightarrow \mathrm{}{\int }_v^0?dV=-{\int }_x^{\mathrm{\infty }}?gdx$

$\Rightarrow \mathrm{}O-V=-\left[\int \frac{Ax}{{\left(a^2+x^2\right)}^{3/2}}\right]$

Let, $a^2+x^2=t^2$ ${}^{}{}^{}{}^{}$

$\Rightarrow \mathrm{}2xdx=2tdt$

$\Rightarrow \mathrm{}\mathrm{x}\mathrm{d}x=\mathrm{t}\mathrm{d}\mathrm{t}$

$\Rightarrow \mathrm{}V=\int \frac{Atdt}{t^3}\Rightarrow -\frac{A}{t}\Rightarrow -{\left.\frac{A}{\sqrt[]{a^2+x^2}}\right|}_x^{\mathrm{\infty }}$

$\Rightarrow \mathrm{}V=\frac{A}{\sqrt[]{a^2+x^2}}$

$\mathrm{}\mathrm{q}\mathrm{V}=\frac{1}{2}m{v}^2$

$\Rightarrow \mathrm{v}=\sqrt[]{\frac{2\mathrm{q}\mathrm{V}}{\mathrm{m}}}\Rightarrow \mathrm{v}\propto \sqrt[]{\frac{\mathrm{q}}{\mathrm{m}}}$

$\frac{{\mathrm{v}}_{\mathrm{H}}}{{\mathrm{v}}_{\mathrm{H}\mathrm{e}}}=\sqrt[]{\frac{1}{1}*\frac{4}{1}}=\frac{2}{1}$