Physics

$\widehat{r}-\widehat{i}=2cos\theta \widehat{n}......\left(1\right)$

$\Rightarrow \widehat{r}=\widehat{i}-2\left(\widehat{i}.\widehat{n}\right)\widehat{n}$

$\Rightarrow \overrightarrow{b}=\overrightarrow{a}-2\left(\overrightarrow{a}.\overrightarrow{c}\right)\overrightarrow{c}$

The key difference between these two terms is that displacement current is deprived of electrons which flow in the case of an actual current. It's role is to help generate magnetic field which is produced when the medium changes between two different bodies.

  $N=mgcos30°+qEsin30°$

$a=\frac{mgsin\theta -qEcos\theta -\mu N}{m}=2.30m/s^2$

$S=ut+\frac{1}{2}a{t}^2$

$\Rightarrow t=\sqrt[]{\frac{2\mathcal{l}}{a}}=1.31sec$             

Frequency increases on filing. So, initial frequency of A is 335 Hz.

f = 340 – 5 = 335 Hz

-> $Z=\sqrt[]{R^2+{\left(X_L-X_C\right)}^2}$

$Z=\sqrt[]{{\left(120\right)}^2+{\left(10-100\right)}^2}=150\Omega$

$\omega =\frac{1}{\sqrt[]{LC}}=\frac{1}{\sqrt[]{10^{-1}*10^{-4}}}=\sqrt[]{10^5}$

$?\omega =2\pi f$

$\Rightarrow f=\frac{10^3}{2\pi \sqrt[]{10}}=50Hz$

$A=A_0{e}^{-\lambda t_1}$     [Radio active decay law]

$\frac{A}{5}=A_0{e}^{-\lambda \left(t_2-t_1\right)}$

$\Rightarrow Averagelife=\frac{1}{\lambda }=\frac{\left(t_2-t_1\right)}{\mathcal{l}n5}$  

Stress = Y * strain

-> $\frac{T_1}{A}=Y*-\frac{\left({\mathcal{l}}_1-\mathcal{l}\right)}{\mathcal{l}}\left(i\right)$  

  $\frac{T_2}{A}=Y*\frac{\left({\mathcal{l}}_2-\mathcal{l}\right)}{\mathcal{l}}\left(ii\right)$                          

$\Rightarrow$ $\frac{T_1}{T_2}=\frac{{\mathcal{l}}_1-\mathcal{l}}{{\mathcal{l}}_2-\mathcal{l}}$                      

$\Rightarrow \mathcal{l}=\frac{T_1{\mathcal{l}}_2-T_2{\mathcal{l}}_2}{T_1-T_2}=\frac{T_2{\mathcal{l}}_1-T_1{\mathcal{l}}_2}{T_2-T_1}$            

They work through the principle of Maxwell principle. A changing magnetic field will induce electric current and changing electric field will produce magnetic field, both in oscillating directions perpendicular to each other. Both of them move in different planes, and their interaction produces electromagnetic waves.

$y=\alpha x-\beta x^2$

$\Rightarrow \frac{dy}{dx}=\alpha -2\beta x=0$  

$\Rightarrow x=\frac{\alpha }{2\beta }$           

$y_{max}=\alpha *\frac{\alpha }{2\beta }-\beta *{\left(\frac{\alpha }{2\beta }\right)}^2=\frac{{\alpha }^2}{4\beta }$           

Range = $2x=\frac{\alpha }{\beta }=\frac{2u^{2}sin\theta .cos\theta }{g}$  

On comparing with

y = x tan θ - $\frac{g{x}^2}{2u^{2}co{s}^2\theta }$  

mg – T = ma       . (1)

T * R = l a               . (2)

a = a R                    . (3)

With the help of equations (1), (2) and (3), we get

-> $a=\frac{mg}{m+\frac{l}{R^2}}$  

$v=\sqrt[]{2ah}=\omega R$  

$\Rightarrow {\omega }^2=\frac{2mgh}{l+m{R}^2}$