Physics

An excellent example of pure rotational motion is the motion of the blades of a ceiling fan when it is switched on. In this type of motion, the object rotates about a fixed axis, and all particles of the object move in circles centred on that axis. Windmills and turbines also follow the same rotational mechanics. 

${\upsilon }_0=320Hz.v_{train}=36km/h=\frac{36*1000}{60*60}=10m/s$

${\upsilon }_{\left(reflectedSound\right)}={\upsilon }_0\left(\frac{v}{v-v_{train}}\right)$

$=320\left(\frac{330}{330-10}\right)=330Hz$

$\Rightarrow {\upsilon }_{echo}={\upsilon }_{reflected}\left(\frac{v+v_{train}}{V}\right)$

$=330\left(\frac{330+10}{330}\right)=340Hz.$

$P_1=1.2*10^{-30}C.m{P}_2=2.4*10^{-30}C.m$

$E_1=5*10^{4}N{C}^{-1}{E}_2=15*10^{4}N{C}^{-1}$

So, $\frac{{\tau }_1}{{\tau }_2}=\frac{P_1{E}_{1}sin90°}{P_2{E}_{2}sin90°}=\frac{\left(1.2*10^{-30}\right)*\left(5*10^4\right)}{\left(2.4*10^{-30}\right)*\left(15*10^4\right)}$

$=\frac{1}{2}*\frac{1}{3}=\frac{1}{6}\Rightarrow x=6$

$R_{AB}=20\Omega$

L = 300 cm

Null point is at 60 cm from A, so

$20mV=\frac{4}{R+20}*20*\left(\frac{60}{300}\right)*10^3$

$\Rightarrow 20=\frac{16}{R+20}*10^3$

$R=\frac{15600}{20}=780\Omega$

 $\frac{{}_{}}{\text{exception 25:}}$ $i=\frac{{\mathcal{l}}_0}{\sqrt[]{2}}$  at ${\omega }_1$ ${}_{}$ = 212 rad/s $R=5\Omega$ $$

${}_{}$  ${\omega }_2$ = 232 rad/s $\Delta \omega ={\omega }_2-{\omega }_1=20rad/s$ ${}_{}{}_{}$

$P=\frac{P_{max}}{2}at{\omega }_{1}and{\omega }_2$

So, $\Delta \omega ={\omega }_2-{\omega }_1=\frac{R}{L}$ ${}_{}{}_{}\frac{}{}$

$\Rightarrow L=\frac{R}{\Delta \omega }=\frac{5}{20}=.25H$

= 250 mH

Rotational motion in Class 11 Physics is regarded as a challenging chapter, particularly due to the transition from point particles to extended bodies. Additionally, the concepts covered here are analogous to, yet distinct from, linear motion. Even vector calculations here can be difficult. But the key to mastering this chapter is to be conceptually clear with your previous chapters in Physics. You also need to be able to visualise rotational motion instead of memorising definitions, to be able to master it.  

${\lambda }_1=560nm,$ fringe width, B = 7.2 mm

$\Rightarrow B_1=\frac{D{\lambda }_1}{d}=7.2mm$

For ${\lambda }_2\to B_2=\frac{D{\lambda }_2}{d}=8.1mm$ ${}_{}{}_{}\frac{{}_{}}{}$

$\frac{B_2}{B_1}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{8.1}{7.2}\Rightarrow {\lambda }_2\frac{81}{72}{\lambda }_1$

$=\frac{9}{8}*560nm$

= 630 nm

Yes, rotational motion is important for the NEET exam. Expect and prepare for, at least, two to three questions on rotational motion as per the latest NEET Physics syllabus for Mechanics. Questions from this chapter are clubbed into the application of principles from other areas of mechanics, such as Laws of Motion, Work, Energy, and Power, and Conservation of Momentum. 

t_1/2 = 2hr 30 min

Radiation intensity a disintegrations / sec (Activity)

As,   $A=\frac{A_0}{{2^t}^{\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$

For safe working, $A=\frac{A_0}{64}\Rightarrow \frac{A_0}{64}=\frac{A_0}{2^{\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$}\right.}}$  

$\Rightarrow t=6t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=6*2.5hr$                            

= 15