Physics

Gravitational constant $=\left. [{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]$

Gravitational potential energy $=\left. [{\mathrm{M}\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

Gravitational potential $=\left. [{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

Gravitational intensity $=\left. [{\mathrm{L}\mathrm{T}}^{-2}\right]$

Root mean square speed of gas molecules

${\nu }_{\text{rms}}=\sqrt[]{\frac{3RT}{M}}$

Pressure exerted by ideal Gas

$\mathrm{P}=\frac{1}{3}\rho v_{\mathrm{r}\mathrm{m}\mathrm{s}}^2$

$\mathrm{P}=\frac{1}{3}\mathrm{m}\mathrm{n}{\nu }^2$

$\rho =\mathrm{m}\mathrm{n},{\mathrm{v}}_{\mathrm{r}\mathrm{m}\mathrm{s}}^2={\nu }^{-2}$

Average kinetic energy of a molecular

$\mathrm{K}\mathrm{E}=\frac{3}{2}\mathrm{K}\mathrm{T}$

Total internal energy of 1 mole of a diatomic gas

$\mathrm{U}=\frac{\mathrm{f}}{2}\mu \mathrm{R}\mathrm{T}$

$\mathrm{U}=\frac{5}{2}\mathrm{R}\mathrm{T}$ (For 1 mole diatomic gas)

Mass $=\mathrm{M}$

Density of ball $=\mathrm{d}$

Density of glycerine $=\frac{\mathrm{d}}{2}$

${\mathrm{F}}_{\mathrm{B}}={\mathrm{V}}_{\mathrm{s}}{\rho }_{\mathcal{l}}\mathrm{g}=\mathrm{V}\frac{\mathrm{d}}{2}\mathrm{g}$

${\mathrm{F}}_{\mathrm{g}}=\mathrm{M}\mathrm{g}=\mathrm{v}\mathrm{d}\mathrm{g}$

For constant velocity, ${\mathrm{F}}_{\text{net}}=0$

$\therefore {\mathrm{F}}_{\mathrm{B}}+{\mathrm{F}}_{\mathrm{v}}=\mathrm{M}\mathrm{g}$

${\mathrm{F}}_{\mathrm{V}}=\mathrm{M}\mathrm{g}-{\mathrm{F}}_{\mathrm{B}}=\mathrm{V}\mathrm{d}\mathrm{g}-\frac{\mathrm{V}\mathrm{d}\mathrm{g}}{2}=\frac{\mathrm{V}\mathrm{d}\mathrm{g}}{2}=\frac{\mathrm{M}\mathrm{g}}{2}$

$\begin{array}{rr}& \mathrm{V}=\left(\text{no. of moles}\right)\left(22.4\text{litre}\right)\\ & =\frac{\text{mass}}{\text{molar mass}}\left(22.4*{10}^{-3}{\mathrm{m}}^3\right)\\ & =\frac{4.5*{10}^3}{18}*22.4*{10}^{-3}{\mathrm{m}}^3\\ & =5.6{\mathrm{m}}^3\end{array}$

Polar molecules have centres of positive and negative charges separated by some distance, so they have permanent dipole moment

(n) $\left(1.1\right)=(\mathrm{n}+1)$

$0.1\left(\mathrm{n}\right)=1$

$\mathrm{n}=10$

Required number of oscillation $=n+1=10+1=11$

$\stackrel{?}{\mathrm{v}}?\stackrel{?}{\mathrm{E}}*\stackrel{?}{\mathrm{B}},\stackrel{\mathrm{ˆ}}{\mathrm{v}}=\stackrel{\mathrm{ˆ}}{\mathrm{i}}$

Option (1) $\stackrel{?}{\mathrm{E}}*\stackrel{?}{\mathrm{B}}=\stackrel{?}{0}\stackrel{?}{\mathrm{E}}?\stackrel{?}{\mathrm{B}}$

Option (2) $\stackrel{?}{\mathrm{E}}*\stackrel{?}{\mathrm{B}}=2\stackrel{\mathrm{ˆ}}{\mathrm{i}}$ parallel to $\stackrel{?}{\mathrm{v}}$

Option (2) $\stackrel{?}{\mathrm{E}}*\stackrel{?}{\mathrm{B}}=\stackrel{?}{0}\stackrel{?}{\mathrm{E}}\Uparrow \stackrel{?}{\mathrm{B}}$

Option (2) $\stackrel{?}{\mathrm{E}}*\stackrel{?}{\mathrm{B}}=\stackrel{?}{0}\stackrel{?}{\mathrm{E}}?\stackrel{?}{\mathrm{B}}$

$\omega =100$

$v=\frac{\omega }{2\pi }=\frac{100}{2\pi }=\frac{50}{\pi }\mathrm{H}\mathrm{z}$

Resonance frequency

$v_0=\frac{1}{2\pi \sqrt[]{\mathrm{L}\mathrm{C}}}=\frac{1}{2\pi }\sqrt[]{\frac{1}{10*10*{10}^{-6}}}$

$=\frac{50}{\pi }\mathrm{H}\mathrm{z}$

${\mathrm{Y}}_{\text{copper}}<{\mathrm{Y}}_{\text{steel}}$

$\frac{E_1}{E_2}=\frac{?{\mathcal{l}}_1}{?{\mathcal{l}}_2}$

$\frac{1.5}{2.5}=\frac{36}{{\mathcal{l}}_2}\Rightarrow {\mathcal{l}}_2=36*\frac{5}{3}=60\mathrm{c}\mathrm{m}$