Chapter 8, Problem 7RAT

Consider two mercury barometer, one having a cross-sectional area of $1{\text{cm}}^{\text{2}}$ and the other $2{\text{cm}}^{\text{2}}$ . Mercury in the smaller tube will rise

(a) to the same height as the other.

(b) twice as high as the other.

(c) four times as high as other.

(d) None of these.

Solution

To determine: The correct option for the statement “Consider two mercury barometer, one having a cross-sectional area of $1{\text{cm}}^{\text{2}}$ and the other $2{\text{cm}}^{\text{2}}$ . Mercury in the smaller tub will rise”.

Answer:

The correct option for the statement “Consider two mercury barometer, one having a cross-sectional area of $1{\text{cm}}^{\text{2}}$ and the other $2{\text{cm}}^{\text{2}}$. Mercury in the smaller tub will rise” is option (a).

Explanation:

In a barometer, the mercury is used as a working fluid. Mercury is convenient because it is more massive and denser than water. The water is less heavy and will be lifted by air pressure to a much higher tube level.

The rise in the height of fluid level is dependent upon the pressure in the tube, density of the fluid and the gravitational acceleration. The rising level of fluid in barometer does not depend upon the cross-section.

Thus, the rising level of mercury in a barometer does not depend upon the cross-sectional area of the barometer mercury in the smaller tube cross-section will rise to the same height as the other.

Conclusion:

The correct option for the statement “Consider two mercury barometer, one having a cross-sectional area of $1{\text{cm}}^{\text{2}}$ and the other $2{\text{cm}}^{\text{2}}$. Mercury in the smaller tub will rise” is option (a).