On 0°C pressure measured by barometer is 760 mm. What will be pressure on 100°C

The correct option is None of these.

Let us analyze the behavior of a barometer as temperature increases. When the temperature increases from $0°\text{C}$ to $100°\text{C}$, two main effects occur:
1. The mercury inside the barometer expands, which decreases its density.
2. The glass tube containing the mercury also expands, increasing its volume.

Generally, the pressure of a column of fluid is given by:
$P=h\rho g$
where $h$ is the height of the mercury column, $\rho$ is the density of mercury, and $g$ is the acceleration due to gravity.

Because mercury has a relatively high coefficient of volume expansion ($\gamma \approx 1.8\times {10}^{-4}/°\text{C}$), its density decreases significantly as temperature increases. Specifically, the density at a higher temperature $T$ is related to the density at $0°\text{C}$ by:
${\rho }_T=\frac{{\rho }_0}{1+\gamma \Delta T}$

For a constant atmospheric pressure, the measured height $h^{\text{'}}$ of the mercury column must increase to compensate for the reduced density:
$h^{\text{'}}=h_0(1+\gamma \Delta T)$

Substituting $h_0=760\text{mm}$, $\gamma \approx 1.8\times {10}^{-4}/°\text{C}$, and $\Delta T=100°\text{C}$:
$h^{\text{'}}\approx 760\times (1+1.8\times {10}^{-4}\times 100)=760\times (1+0.018)=760\times 1.018\approx 773.7\text{mm}$

If the question refers to the actual atmospheric pressure remaining constant, then the corrected pressure reading represents the same standard pressure (760 mm of Hg at $0°\text{C}$). If it refers to the observed height of the column, it increases to approximately 773.7 mm. Since none of the specific values (760 mm, 730 mm, 780 mm) match this physical adjustment, the correct choice is None of these.