Units and Measurement

${\mu }_0=\frac{B_0}{H}=N{A}^{-2}$

$\left[{\mu }_0\right]=\left[M^1{L}^1{T}^{-2}{A}^{-2}\right]$

It is not dimensionless

R_H : m^-1

h : kgm² s^-1

${\mu }_B:kg{m}^{-1}{s}^{-2}$          

$\eta :kg{m}^{-1}{s}^{-1}$              

$\frac{\Delta z}{z}*100=3\frac{\Delta x}{x}*100+\frac{1}{2}\frac{\Delta y}{y}*100$

$=3*4+\frac{1}{2}*12$

$=\left(12+6\right)\mathrm{\%}$

$=18\mathrm{\%}$

$P=E{L}^2{M}^{-5}{G}^{-2}$

$=\left[M{L}^2{T}^{-2}\right]{\left[M{L}^2{T}^{-1}\right]}^2\left[M^{-5}\right]{\left[M^{-1}{L}^3{T}^{-2}\right]}^{-2}$

$=M^0{L}^0{T}^0$

Pitch = 0.5 mm

Least count = $\frac{pitch}{division}=\frac{0.5mm}{50}=0.01mm$ $\frac{}{}\frac{}{}$

True Reading = 5mm + 20 * 0.01 – 5 * 0.01 = 5.15 mm

$z=\frac{A^2{B}^3}{C^4}$

The relative error in z is given by

$\frac{\Delta z}{z}=\frac{2\Delta A}{A}+\frac{3\Delta B}{B}+\frac{4\Delta C}{C}$

$\frac{\Delta z}{z}*100=3\frac{\Delta x}{x}*100+\frac{1}{2}\frac{\Delta y}{y}*100$

$=3*4+\frac{1}{2}*12$

$=\left(12+6\right)\mathrm{\%}$

$=18\mathrm{\%}$

A. Torque $\underset{}{\overset{}{\to }}$  (iii) Nm

B. Stress $\underset{}{\overset{}{\to }}$ (iv) Nm^-2

C. Latent Heat $\underset{}{\overset{}{\to }}$ (ii) J kg^-1

D. Power $\underset{}{\overset{}{\to }}$ (i) Nm S^-1

Given, m = 0.6 $\pm$ $$ 0.006

$\Rightarrow p=\frac{m}{v}=\frac{m}{\pi r^2\mathcal{l}}$

$\frac{\Delta \rho }{\rho }*100=\frac{\Delta m}{m}*100+2\frac{\Delta r}{r}*100+\frac{\Delta \mathcal{l}}{\mathcal{l}}*100$

= 1 + 2 * 1 + 1

Let $V_{R{G}_r}$ ${}_{{}_{}}$ (velocity of Rain w.r.t. ground or w.r.t to standing Girl)

${\overrightarrow{V}}_{R{G}_r}=V_x\widehat{i}+V_y\widehat{j}$

$tan\left(270+45°\right)=-cot45°=\frac{V_y}{V_x}=-1$

Now, velocity of Rain w.r.t. moving Girl

${\overrightarrow{V}}_{R{G}_m}=\left(V_x-15\sqrt[]{2}\right)\widehat{i}+V_y\widehat{j}=\left(15\sqrt[]{2}-15\sqrt[]{2}\right)\widehat{i}+V_y\widehat{j}=V_y\widehat{j}$

${\overrightarrow{V}}_{R{G}_m}=-15\sqrt[]{2}\widehat{j}\Rightarrow {\overrightarrow{V}}_{R{G}_m}=\frac{-30}{\sqrt[]{2}}\widehat{j}\Rightarrow \left|{\overrightarrow{V}}_{R{G}_m}\right|=\frac{30}{\sqrt[]{2}}$