Physics

Angular momentum imparted to sprinkler per

$second=vr\frac{dm}{dt}=\frac{0.6}{60}*0.5*1=0.005N.m$

$?l\frac{d\omega }{dt}=0.005$

$?\frac{d\omega }{dt}=\frac{0.005}{500*{10}^{-7}}$

$=100\frac{rad}{s^2}$

Applying conservation of momentum for collision of blocks

$2mv+0=3m{v}^{\text{'}}$

$?v^{\text{'}}=\frac{2v}{3}\dots \left(1\right)$

Now, from conservation of energy

$\frac{1}{2}*3m*{v^{\text{'}}}^2=\frac{1}{2}k{x}_0^2$

$x_0=\sqrt[]{\frac{3m{v}^{\text{'}2}}{k}}=v\text{'}\sqrt[]{\frac{3m}{k}}$

$=\frac{2v}{3}\sqrt[]{\frac{3m}{k}}=v\sqrt[]{\frac{4m}{3k}}$

For normal emergence

$r=A$

From Snell's Law

$\frac{\sin ?i}{\sin ?r}=\frac{\mu }{1}$

$?\sin ?i=\sqrt[]{2}\sin ?{30}^0$

$?i={45}^0$

Balancing torque about COM

$T_A\left(\frac{l}{2}\right)=T_B\left(\frac{l}{6}\right)$

$?\frac{T_A}{T_B}=\frac{1}{3}$

$\theta =\omega t$

$2\pi =\left(\frac{V}{3R}\right)T$

$?t=\frac{6\pi R}{V}$

The distance travelled by car in this time is

$s=vt$

$?s=v\left(\frac{6\pi R}{V}\right)$

$=6\pi R$

It depends on the requirement. But in most cases, AC generator will be preferred over a DC one. DC generator can be useful in cases where you just require a continuous supply of current without any disturbance. But if you want a good quality current to be transmitted over longer distances for significant period of time, go for an AC generator. AC generators are much more reliable and also have longer life durations.

Magnify power of telescope for far point is given as

$m=\frac{{\theta }_i}{{\theta }_0}=\frac{f_0}{f_e}$

$?{\theta }_i={\theta }_0\left(\frac{f_0}{f_e}\right){=1}^0\left(\frac{100}{5}\right)={20}^0$

For thin prism, deviation  $=\left(\mu -1\right)A$

The key difference between these two is slip rings are the rings used in an AC generator for generating AC current. While commutators are used in DC generators to produce DC current. If we talk about the shape, slip ring is a continuous circle while commutator is divided into two halves.