Physics

Emf = $\frac{-d?}{dt}$ $\frac{}{}$

When magnet passes through the centre rogion of loop, no emf is induced and the polarity of emf will be negative while entering the loop.

F. B. D of Beaker

By NLM2    

$\begin{array}{l}f=ma=m{\omega }^{2}R\\ \Rightarrow m{\omega }^{2}R\le \mu N\\ R\le \mu g/{\omega }^2\end{array}$

PT³ = k (constant)

$\Rightarrow \left(\frac{nRT}{V}\right)T^3=k$

$\Rightarrow T^4{V}^{-1}=k$

$\Rightarrow T^4=kV$

$\Rightarrow 4*\frac{\Delta T}{T}=\frac{\Delta V}{V}$ - (i) >

$\Rightarrow \Delta V=VY\Delta T$ - (ii) >

Comparing I > & ii >

$\Rightarrow Y=\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$T$}\right.$

dA = 2r dr

$dq=\sigma *2\pi rdr$

$\Rightarrow E={\displaystyle \underset{0}{\overset{R}{\int }}\frac{kdqz}{{\left(z^2+r^2\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

$\Rightarrow E=\frac{\sigma }{2{\epsilon }_0}\left[1-\frac{z}{\sqrt[]{R^2+z^2}}\right]$

$P=\rho RT$

$\Rightarrow \frac{{\rho }_1}{{\rho }_2}=\frac{P_1}{P_2}*\frac{T_2}{T_1}=\frac{76}{45}*\frac{260}{300}$

$\Rightarrow \frac{{\rho }_1}{{\rho }_2}=\frac{M_1}{M_2}$

$\Rightarrow M_2=\frac{45*300*185}{76*266}=123.54kg$

$X_P\left(t\right)=\alpha t+\beta t^2$

$V_P\left(t\right)=\alpha +2\beta t$  - (i)

$X_Q\left(t\right)=ft-t^2$

$V_Q\left(t\right)=f-2t$ - (ii)
(i) = (ii)

$\alpha +2\beta t=f-2t\Rightarrow t\left(2\beta +2\right)=f-\alpha$

$t=\frac{f-\alpha }{2\left(\beta +1\right)}$

First angle, θ₁= θ, $R=\frac{u^{2}sin2\theta }{g}$      

Another angle (θ₂ = 90 - θ) for which range will be Same as that of θ₁ =θ

$R^1=\frac{u^{2}sin2\left(90-\theta \right)}{g}=\frac{u^2}{g}sin2\theta =R$

at ${\theta }_1=\theta ,h_1=\frac{u^{2}si{n}^2\theta }{2g}$

$\&{\theta }_2=90-\theta ,h_2=\frac{u^{2}si{n}^2{\theta }_2}{2g}=\frac{u^{2}co{s}^2\theta }{2g}$

$\Rightarrow h_1{h}_2=\frac{1}{4^2}{\left[\frac{u^{2}sin2\theta }{g}\right]}^2$

$h_1{h}_2=\frac{1}{4^2}{R}^2$

$R=4\sqrt[]{h_1{h}_2}$

So, Both statement is true & Reason is correct explanation for statement 1.

A beat wave arises due to constructive and destructive interference between two sound waves. These two frequencies have nearly equal frequencies but never the same. The resulting amplitude envelope oscillates at the beat frequency.  

Beats form when two harmonic waves of nearly equal frequencies and identical amplitudes travel in the same direction, whic allows the superposition of waves. 

Beat frequency is the rate of amplitude modulation we hear when two wave frequencies, f1 and f2 interfere. It's given by |f1-f2|. It represents how fast the loudness oscillates over time.