physics-class-11-unit-08-chapter-03-determination-of-gravitational-constant-lecture-3-7-6ivb2wnpafu

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Determination of Gravitational Constant </primary>
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- 1.Newton's Laws of Motion $2^{\text {nd }}$ and $3^{\text {rd }}$ Laws
- 2.Centripetal Force

- Example: The center of the orbit from the sun to that from the earth to that of the sun.

- $F_c=\frac{m v^2}{r}$

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<footer style = "font-size: 18px"> $\rightarrow$ Determination of Gravitational Constant $\rightarrow$ <span style = "color:blue"> Determination of Gravitational Constant </span> $\rightarrow$ Galilean Law $\rightarrow$ Galilean Law </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Galilean Law </primary>
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- Two bodies start with a separation d.

- The distance between them should keep on decreasing as they fall towards because both of them fall towards the center.

- Acceleration should increase.

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<footer style = "font-size: 18px">Galilean Law $\rightarrow$ Galilean Law $\rightarrow$ <span style = "color:blue"> Galilean Law </span> $\rightarrow$ Acceleration Due to Gravity at Height $\rightarrow$ Acceleration Due to Gravity at Height </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Acceleration Due to Gravity at Height </primary>
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- $m {{a}}=\frac{G m M_E}{\left(R_E+{{h}}\right)^2}$

- $\frac{h}{R_E} \ll 1$

- $a=\frac{G M_E}{h^2}\left[\frac{1}{\left(1+\frac{h}{R_E}\right)^2}\right]$

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<footer style = "font-size: 18px">Galilean Law $\rightarrow$ Galilean Law $\rightarrow$ <span style = "color:blue"> Acceleration Due to Gravity at Height </span> $\rightarrow$ Acceleration Due to Gravity at Height $\rightarrow$ Acceleration Due to Gravity at Height </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Acceleration Due to Gravity at Height </primary>
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- $x=\frac{h}{R_E} \ll 1$

- So, $\frac{1}{\left(R_E+h\right)^2}$

- $=\frac{1}{R_E^2\left(1+\left(\frac{h}{R_E}\right)\right)^2}=\frac{1}{R_E^2(1+x)^2}$

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<footer style = "font-size: 18px">Galilean Law $\rightarrow$ Acceleration Due to Gravity at Height $\rightarrow$ <span style = "color:blue"> Acceleration Due to Gravity at Height </span> $\rightarrow$ Acceleration Due to Gravity at Height $\rightarrow$ Acceleration Due to Gravity at Height </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Acceleration Due to Gravity at Height </primary>
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- $h=100 \mathrm{~m}$

- $R_E=6.4 \times 10^6$

- $x$ is really small

- Reconciled all aspects of law of freely falling body with the Netonian law

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<footer style = "font-size: 18px">Acceleration Due to Gravity at Height $\rightarrow$ Acceleration Due to Gravity at Height $\rightarrow$ <span style = "color:blue"> Acceleration Due to Gravity at Height </span> $\rightarrow$ Acceleration Due to Gravity at Height $\rightarrow$ Cavendish Experiment </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Cavendish Experiment </primary>
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- The whole Apparatus was placed in a thick wooden box.

- The wooden box was enclosed in a shed.

- Observations were made through two small holes fitted with telescopes.

- The experiment was not null. A Large period of $20 \mathrm{~min}$.

- The vernier scale had a least count of $0.1 \mathrm{~mm}$.

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<footer style = "font-size: 18px">How To Determine Forces $\rightarrow$ Cavendish Experiment $\rightarrow$ <span style = "color:blue"> Cavendish Experiment </span> $\rightarrow$ Cavendish Experiment $\rightarrow$ Experimental Details </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Cavendish Experiment </primary>
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| Column 1 | Column 2 | Column 3 | Column 4 |
| -------- | -------- | -------- | -------- |
| Mass of large ball    | $m_W$     | 2439000 grains   | 158.04 kg   |
| Mass of small ball    | $m_b$     | 11262 grains  | 0.73 kg   |
| Mass of supporting rod - insertial (equivalent small ball mass)    | $m_I.rod$     | 398 grains | .03 kg    |
| Mass of supporting rod - gravitational (equivalent small ball mass)    | $m_G.rod$     | 157 grains | .01 kg    |
| Mass of copper rods (equivalent small ball mass)    | $m_copper$     | 18800 grains | 1.22 kg    |
| Distance between large ball    | L     | 73.30 in | 1.860 kg    |

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<footer style = "font-size: 18px">Cavendish Experiment $\rightarrow$ Cavendish Experiment $\rightarrow$ <span style = "color:blue"> Cavendish Experiment </span> $\rightarrow$ Experimental Details $\rightarrow$ Experimental Value </footer>

### <Success style="font-size:25px"> Determination Of Gravitational Constant L-3 </Success>
### <primary style="font-size:24px"> Experimental Value </primary>
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- The distance between small rod and the big rod = 0.225 millimeter.

- We want a very large gravitational force. Therefore, the distance must be as small as possible.

- Measure the angle.

- Make an analysis and find out how determine the value of G.

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<footer style = "font-size: 18px">Cavendish Experiment $\rightarrow$ Experimental Details $\rightarrow$ <span style = "color:blue"> Experimental Value </span> $\rightarrow$ Analysis $\rightarrow$ Analysis </footer>