Question

A simple barometer reads 75 cm mercury. A drop of alcohol is introduced into it, which raises the mercury column. The new barometric height will be:

• A. 75 cm
• B. Less than 75 cm
• C. More than 75 cm
• D. None of the above

Answer 1

The correct option is B

Less than 75 cm

Explanation for the correct option

Step 1. Given data

The initial level of the mercury column, $h_{1_{}}=75cm$

Step 2. Assumptions

Let the final level of mercury $=h_2$

Let the initial pressure $=p_1$

Let the final pressure $=p_2$

Let the initial volume $=v_1$

Let the final volume $=v_2$

Let the density of mercury $=\rho$

Let the temperature remains the same.

Step. 3 Depicting whether the level of mercury will rise or fall on adding a drop of alcohol.

From Boyles's law, we have

$p_1{v}_1=p_2{v}_2$

But, $p=h\rho g$

Therefore, $h_1\rho g{v}_1=h_2\rho g{v}_2$

Clearly, $h_2\propto \frac{1}{v_2}$

The rise of mercury will be inversely proportional to the volume.

Hence, when we add a drop of alcohol, volume increases which causes a reduction in the barometric height.

Hence, option (b) will be correct.