# 85-Q1: Relative Density of a Liquid¶

Time: $$1 \frac{1}{2}$$ hr.

## Apparatus¶

Metre rule; thread ($$\approx 50\text{cm}$$.; fulcrum (eg. prism); fulcrum support (height $$\approx$$ $$10\text{cm}$$; $$L_1$$ $$200\text{ml}$$ water in $$250\text{m}$$ beaker; $$L_2$$ $$200\text{ml}$$ motor oil (or kerosene) in $$250\text{ml}$$ beaker; $$W_1$$ $$50\text{g}$$ mass (metal); $$W_2$$ $$20\text{g}$$ mass (plastic or rubber); piece of chalk; 2 sheets graph paper.

In this experiment you are required to determine the density of liquid $$L_2$$ relative to that of liquid $$L_1$$, and find the mass $$M$$ of the metre rule provided. Proceed as follows:

1. Locate and mark the centre of gravity $$G$$ of the metre rule.
2. Set up the apparatus as illustrated below, where $$a = 5$$cm, and $$W_1$$ and $$W2$$ are masses of $$50\text{g}$$ and $$20\text{g}$$ respectively.

1. With $$W_2$$ totally immersed in liquid $$L_1$$ and $$x = 10\text{cm}$$, balance the metre rule by adjusting the position of $$W_1$$. Read and record distance $$y$$. Repeat the process for $$X = 20\text{cm}, 30\text{cm}, 40\text{cm}, 50\text{cm}, \text{ and } 54\text{cm}$$. Tabulate the values of $$x$$ and $$y$$. (7 marks)
2. Replace liquid $$L_1$$ by liquid $$L_2$$ and then repeat the procedure outlined in (c) above. (7 marks)
3. Plot a graph of $$y$$ vs. $$x$$ using the table obtained in (c). (8 marks)
4. Read and record $$I$$, the value of $$y$$ when $$x = 0$$. Calculate $$10 \times I$$, which is equal to the mass of the metre rule. (4 marks)
1. Find the slope $$S_1$$ of the graph. (4 marks)
2. Find the value of $$\lambda _1$$ given that $$\lambda_1 = 0.4 - S_1$$. (2 marks)
1. Plot a graph of $$y$$ against $$x$$ using the table obtained in (d). (8 marks)
2. Find the slope $$S_2$$ of this graph. (4 marks)
1. Find the value of $$\lambda _2$$ given that $$\lambda _2 = 0.4 - S_2$$. (2 marks)
2. Evaluate the ratio $$\frac{\lambda _2}{\lambda _1}$$, which is equal te the density of liquid $$L_2$$ relative to that of liquid $$L_1$$. (4 marks)