To determine the centre of gravity, G, of the metre rule:

Here are the instructions for the experiment and the definitions:

a)

(i) To determine the centre of gravity, G, of the metre rule:
Balance the metre rule horizontally on a knife edge. The point on the rule where it balances without tipping is its centre of gravity, G.

(ii) To suspend the metre rule as shown in Fig. 1:
Clamp the metre rule horizontally at points A and B using two retort stands. Ensure the rule is level. Position a vertical metre rule next to point G to measure its height.

(iii) To measure and record $h_0$:
Read the initial height of the centre of gravity, G, from the vertical metre rule. This is $h_0$.

(iv) To hang mass, $m=100$ g at G:
Carefully suspend a mass of 100 g from the centre of gravity, G, of the metre rule.

(v) To measure and record $h_f$:
After the metre rule has settled, read the new, final height of the centre of gravity, G, from the vertical metre rule. This is $h_f$.

(vi) To evaluate $H = |h_f - h_0|$:
Calculate the depression H by finding the absolute difference between the final height ($h_f$) and the initial height ($h_0$).

$$H = |h_f - h_0|$$

(vii) To repeat the procedure for four other values of $m = 150$ g, 200 g, 250 g and 300 g:
Remove the 100 g mass. Repeat steps (iv) to (vi) for each of the new mass values (150 g, 200 g, 250 g, and 300 g), ensuring to record the corresponding $h_f$ and calculate $H$ for each.

(viii) In each case measure and record $h_f$:
For each mass value, measure and record the final height $h_f$ of the centre of gravity G after the mass is applied.

(ix) Evaluate H:
For each mass value, calculate the depression $H = |h_f - h_0|$.

(x) To tabulate the results:
Create a table with the following columns: | Mass, $m$ (g) | Initial height, $h_0$ (cm) | Final height, $h_f$ (cm) | Depression, $H = |h_f - h_0|$ (cm) | |---|---|---|---| | 100 | | | | | 150 | | | | | 200 | | | | | 250 | | | | | 300 | | | |

(xi) To plot the graph of m on the vertical axis and H on the horizontal axis:
Draw a graph with the values of mass ($m$) on the vertical (y) axis and the values of depression ($H$) on the horizontal (x) axis. Plot the points from your table and draw a line of best fit.

b)

(i) Define Young's Modulus.
Young's Modulus ($E$) is a measure of the stiffness or elasticity of a material. It quantifies the material's resistance to elastic deformation under tensile or compressive stress. It is defined as the ratio of stress ($\sigma$) to strain ($\epsilon$) in the elastic region:

$$E = \frac{\text{Stress}}{\text{Strain}} = \frac{\sigma}{\epsilon}$$

The unit for Young's Modulus is Pascals (Pa) or Newtons per square meter ($\text{N/m}^2$).

$$\boxed{\text{Young's Modulus is the ratio of stress to strain.}}$$

(ii) How does Young's modulus affect the stiffness of a material?
A material with a higher Young's Modulus is stiffer and more resistant to deformation. This means it requires a greater amount of stress to produce a given amount of strain. Conversely, a material with a lower Young's Modulus is less stiff and deforms more easily under stress.

$$\boxed{\text{A higher Young's Modulus indicates a stiffer material.}}$$