physics-class-11-unit-08-chapter-02-conservation-law-fundamental-forces-estimation-of-distances-2-7-db7mxseldlc

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Gravitation </primary>
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* It is assumed that the applied force is known.

* Case of simple harmonic motion: $F=-k x $.

* Case of electrostatic interaction: $F=\frac{e^2}{r^2} \hat{r} $ = $\frac{1 e_1 e_2}{4 \pi \epsilon_0 r^2} \hat{r} $

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<footer style = "font-size: 18px"> $\rightarrow$ CONSERVATION LAWS, FUNDAMENTAL FORCES, ESTIMATION OF DISTANCES $\rightarrow$ <span style = "color:blue"> Gravitation </span> $\rightarrow$ Work done $\rightarrow$ Work done </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Work done </primary>
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- $\vec{F}$ acts in a particle and the body moves.

- $W = \int^{t_2}_{t_1} \vec{F}\cdot d\vec{s}$.

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<footer style = "font-size: 18px">CONSERVATION LAWS, FUNDAMENTAL FORCES, ESTIMATION OF DISTANCES $\rightarrow$ Gravitation $\rightarrow$ <span style = "color:blue"> Work done </span> $\rightarrow$ Work done $\rightarrow$ Work done </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Work done </primary>
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* $F=-\frac{d V(r)}{d r} $

- <span style="color:green">This is the statement of conservation of energy. </span>

- $\Rightarrow \frac{1}{2} m \vec{v}^2+V(r)$ = Constant

- <span style="color:green">$\frac{1}{2} m \vec{v}^2$ = Kinetic Energy</span>
 
- <span style="color:blue"> $V(r)$ = Potential Energy</span>

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<footer style = "font-size: 18px">Work done $\rightarrow$ Work done $\rightarrow$ <span style = "color:blue"> Work done </span> $\rightarrow$ Fundamental Forces $\rightarrow$ Fundamental Forces </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Fundamental Forces </primary>
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| Interaction  | Range | Strength |
| -------- | -------- | -------- |
|  Gravitation   | $\infty$      | $\approx 10^{-37}$     |
| Electromagnetic    | $\infty($ screened $)    |$\approx 10^{-2}$   |
| Nuclear Forces  | $10^{-15} \mathrm{~m}$  | $\approx 1$    |
| Weak Forces    |$<10^{-17} \mathrm{~m}$   | $\approx 10^{-7}$  |

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<footer style = "font-size: 18px">Work done $\rightarrow$ Fundamental Forces $\rightarrow$ <span style = "color:blue"> Fundamental Forces </span> $\rightarrow$ Screening Effect $\rightarrow$ Nuclear Force </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Screening Effect </primary>
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- $F_G \sim \frac{1}{r^2} $

- $F_E \sim \frac{1}{r^2}$

* $F_E$ can be positive and negative.

* Every positive charge likes to get surrounded by negative charges vice-versa.

* Because of this screening, the effective interaction between objects, is very weak compared to the gravitational force.

* The range of electromagnetic forces become smaller.

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<footer style = "font-size: 18px">Fundamental Forces $\rightarrow$ Fundamental Forces $\rightarrow$ <span style = "color:blue"> Screening Effect </span> $\rightarrow$ Nuclear Force $\rightarrow$ Gravitational Force </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Universal Constant </primary>
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- A particle of mass m is moving in the field of the sun's gravitational force.

- Determine the universal constant.

- **$ma = \frac{GMm}{r^2}$**

* mass of A = m

* mass of B = M

* where, <span style="color:green">M >> m</span>

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<footer style = "font-size: 18px">Nuclear Force $\rightarrow$ Gravitational Force $\rightarrow$ <span style = "color:blue"> Universal Constant </span> $\rightarrow$ Distances and Masses $\rightarrow$ Radius of the Earth </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Radius of the Earth </primary>
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- Use trigonometry to find the radius of earth.

- If we know the angle and distance, we should be able to estimate the radius of earth.

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<footer style = "font-size: 18px">Universal Constant $\rightarrow$ Distances and Masses $\rightarrow$ <span style = "color:blue"> Radius of the Earth </span> $\rightarrow$ Radius of the Earth $\rightarrow$ Radius of the Earth Observation and Inference 4th Century BC </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Radius of the Earth </primary>
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- **Simple Example**

- If the earth were flat your range of vision would be infinite.

- We make a simple model and estimate what the radius of the earth.

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<footer style = "font-size: 18px">Distances and Masses $\rightarrow$ Radius of the Earth $\rightarrow$ <span style = "color:blue"> Radius of the Earth </span> $\rightarrow$ Radius of the Earth Observation and Inference 4th Century BC $\rightarrow$ Radius of the Earth </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Radius of the Earth </primary>
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- Point corresponds to Alexandria.

- Point corresponds to Aswan.

- A well in Aswan and well contains water.

- Distance between Alexandria and Aswan is known.

- The distance is 50 stadium.

- $s=R \theta$

- $R = \frac{s}{\theta}$ = 800 km

- $C = 2\pi R $= 40,000 km

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<footer style = "font-size: 18px">Radius of the Earth $\rightarrow$ Radius of the Earth Observation and Inference 4th Century BC $\rightarrow$ <span style = "color:blue"> Radius of the Earth </span> $\rightarrow$ Earth-Moon Distance $\rightarrow$ Earth Sun and Moon Distance </footer>

### <Success style="font-size:25px"> Conservation Law Fundamental Forces Estimation Of Distances L-2 </Success>
### <primary style="font-size:24px"> Earth Sun and Moon Distance </primary>
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* The distance earth,moon and sun can find by  trigonometry.

* The new moon when the moon is completely on the opposite side of the earth.

* The orbit of the moon is slightly inclined to this plane.

*  The moon would come between the earth and the sun. There would have been a solar eclipse.

* Half moon is the eighth day, that day the moon is a perfect semicircle.

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<footer style = "font-size: 18px">Radius of the Earth $\rightarrow$ Earth-Moon Distance $\rightarrow$ <span style = "color:blue"> Earth Sun and Moon Distance </span> $\rightarrow$ Thank You $\rightarrow$  </footer>