Describe the procedure for taking a reading from a vernier caliper, state an advantage of mercury over alcohol in a thermometer, explain the principle of finding the center of gravity using a plumb li

The main scale reading is $5.5 \text{ mm}$.

The thimble scale reading is 47.

Observed reading = Main scale reading + (Thimble scale reading $\times$ Least count)  
Observed reading = $5.5 \text{ mm} + (47 \times 0.01 \text{ mm})$  
Observed reading = $5.5 \text{ mm} + 0.47 \text{ mm}$  
Observed reading = $5.97 \text{ mm}$

Correct reading = Observed reading - Zero error  
Correct reading = $5.97 \text{ mm} - (+0.04 \text{ mm})$  
Correct reading = $5.97 \text{ mm} - 0.04 \text{ mm}$  
Correct reading = $\boxed{5.93 \text{ mm}}$

Mass of rule, $m = 200 \text{ g} = 0.2 \text{ kg}$  
Acceleration due to gravity, $g = 10 \text{ m/s}^2$  
Weight of rule, $W = mg$
$$
W = 0.2 \text{ kg} \times 10 \text{ m/s}^2 = 2 \text{ N}
$$
For a uniform metre rule, its weight acts at its center of gravity, which is at the $50 \text{ cm}$ mark.

Pivot point = $10 \text{ cm}$ mark.  
Distance of weight from pivot, $d_W = 50 \text{ cm} - 10 \text{ cm} = 40 \text{ cm}$.  
Distance of applied force from pivot, $d_F = 65 \text{ cm} - 10 \text{ cm} = 55 \text{ cm}$.

For the rule to be horizontal, the sum of clockwise moments must equal the sum of anticlockwise moments about the pivot.  
Clockwise moment due to weight = $W \times d_W$  
Anticlockwise moment due to applied force = $F \times d_F$
$$
W \times d_W = F \times d_F
$$
$$
2 \text{ N} \times 40 \text{ cm} = F \times 55 \text{ cm}
$$
$$
80 \text{ N cm} = F \times 55 \text{ cm}
$$

$$
F = \frac{80 \text{ N cm}}{55 \text{ cm}}
$$
$$
F = \frac{16}{11} \text{ N}
$$
$$
F \approx 1.4545 \text{ N}
$$
The force which would be applied vertically upward at the $65 \text{ cm}$ mark is $\boxed{1.45 \text{ N}}$ (to 3 significant figures).