The atmospheric pressure decreases by $1cm$ for every $125m$ increase in height.

No, it doesn't depend on the cross-section of the tube.

An aneriod  barometer is made up of a vacuum chamber covered by a thin elastic disk. High atmospheric pressure pushes against the disk and causes it to bulge inward, while low pressure does not push as hard, allowing the disk to bulge outward.

Fortin's barometer is used to measure atmospheric pressure. It is a modified form of Torricelli's simple barometer.

The word 'aneroid' means dry. They are called dry because they do not use any fluid in them. They work on the bulging and compression of diaphragm.

The first reason to use mercury is its high density. The atmospheric pressure measured by mercury barometer is the pressure equal to that at the bottom of the mercury column given by $h\rho g$.

'Aneroid' means dry. Aneroid barometers are those barometers that do no require any fluid to work and measure atmospheric pressure. Hence they are called dry barometers due to this absence of any fluid(specially liquid).

Mercury is the heaviest liquid. Therefore, it rises only to a height of $76cm$ to balance the atmospheric pressure. Water, being $13.6$ times lighter than mercury, will rise to a $13.6$ times larger height. So, the glass tube needs to be much longer.

True. Mercury is used as barometric liquid because it does not vaporise under vacuum condition.

Fortin's barometer is widely used in laboratories and in meteorological departments. Main advantage of Fortin's barometer is it is portable and it allows the mercury level in the cistern to be set to zero. this makes the reading move accurate.

The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. 

Aneroid barometer consists of:

A barometer is an instrument used to measure atmospheric pressure. The two types are liquid and aneroid barometer. Aneroid barometer do not use any liquid.

Mercury barometer has the following disadvantages:

Light needle and system increases sensitivity of the barometer. Frictionless needle improves the efficiency of the system. Pointed needle improves accuracy and removes human errors.

Altimeter is a device used to measure height at a point. It works on the principle of decrease in pressure with an increase in the altitude and actually measures pressure. Aneroid barometers are generally used as altimeter because it is easy to use and carry.

A vernier scale is provided at the top of glass west tube for accurate reading.

Simple barometer is not easy to carry. However, it gives very precise readings. The few drawbacks of simple barometer are counterfeited in an aneroid barometer.

Since the density of mercury is highest in the liquids, it needs smallest column to measure the pressure reducing the size of the equipment and making it easier to use. 

Aneroid barometers are popular for their light weight and size which increases its portability. The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring which is corrugated in form of a diaphragm. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. 

Aneroid barometers are popular for their light weight and size which increases its portability. The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring which is corrugated in form of a diaphragm. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer.  When atmospheric pressure increases, the spring in upper end of box gets depressed and the reading is thus visible due to the elastic potential energy stored in the spring due to compression which pushes the diaphragm inside.

Aneroid barometers are popular for their light weight and size which increases its portability. The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring which is corrugated in form of a diaphragm. Small changes in external air pressure cause the cell to expand or contract. 

Aneroid barometers are popular for their light weight and size which increases its portability. The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring which is corrugated in form of a diaphragm. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer.  Since it is calibrated directly for the atmospheric pressure, no prior adjustments are required to be made before its usage.

Aneroid barometers are popular for their light weight and size which increases its portability. The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring which is corrugated in form of a diaphragm. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer.  When atmospheric pressure increases, the spring in upper end of box gets depressed and the reading is thus visible due to the elastic potential energy stored in the spring due to compression.

Aneroid barometers are those barometers that do not use liquid to tell the atmospheric pressure. They are popular because of the portability due to their small weight and size.The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. 

The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring. Since the instrument calibrated directly to read the atmospheric pressure, small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. 

Aneroid barometers are popular for their light weight and size which increases its portability. The Aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule). The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer.  

The instrument used to measure the altitude is known as altimeter whereas altimetry is defined as the measurement of altitude.

The surface of mercury is shiny and opaque. Therefore it is easily seen while taking the observation. The vapor pressure of mercury is negligible. Hence the barometric height is not affected. The mercury neither sticks nor wets the glass tube.

There will be a very small increase in temperature$.$ The surface area of the combined drop will be smaller than the original combined surface area of the two drops$.$ There is a small amount of work done by the surface tension as it pulls in the excess surface$.$ 

Mercury does not evaporate under vacuum conditions, whereas water does. Hence water is not used in barometers due to this effect whereas mercury is highly preferred.

The atmospheric pressure measured by mercury barometer is the pressure equal to that at the bottom of the mercury column given by $h\rho g$.

All the given properties of mercury shown are true.

The vapor pressure of mercury is negligible. Thus the barometric height of a simple barometer or a mercury barometer is not affected.

Given,

Potential of one small drop of mercury, 
$V=\displaystyle\frac{kq}{r}=20V$
Volume of big drop=volume of $8$ small drops
$\displaystyle\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3\Rightarrow =2r$
$Q'=8q$
Potential of big drop,
$\displaystyle V'=\frac{kQ'}{R}=\frac{K\times 8q}{2r}=\frac{4kq}{r}=4\times 20=80V$
Hence, option $B$ is the correct answer.

Below are the answers:
(a) Mercury in the tube adjusts until the weight of the mercury column balances the atmospheric force exerted on the reservoir. High atmospheric pressure places more force on the reservoir, forcing mercury higher in the column. Low pressure allows the mercury to drop to a lower level in the column by lowering the force placed on the reservoir.
When the tube is pushed down into the trough of mercury the height of mercury column above the surface of the bottom surface remains the same. 

1) It has $13.5$ times higher density than water
2) It doesn't stick to the glass walls of tube like water does.

Atmospheric pressure at the place is equivalent to that of $66cm$ of mercury.
We know that atmospheric pressure at the sea level is equivalent to that of $76cm$ of mercury.
So, pressure at that place is less by $(76-66)=10cm$ of mercury.
We know that atmospheric pressure decreases by $1cm$ for every $125m$ increase in altitude.
So, the concerned place is $(125 \times 10)m=1250m$ above the sea level.

If the top sheet in an aneroid barometer is heavier, it will displace lesser. So, it gives reading corresponding to a lower pressure with a lighter thin sheet. Lower pressure is observed at more heights and hence, the reading of the altimeter will increase.

WATER VAPORISES UNDER VACUUM CONDITIONS.THUS WATER BAROMETER WILL NOT SHOW TRUE ATMOSPHERIC PRESSURE.

Atmospheric pressure at that place is $78cm$ of mercury.
We know that the atmospheric pressure at the sea level is $76cm$ of mercury.
This means, this place has an atmospheric pressure $(78-76)cm=2cm$ more than the atmospheric pressure at the sea level.
We know that the atmospheric pressure increases by $1cm$ for every $125m$ decrease in height.
So, this place is $(125 \times 2)m=250m$ below sea level.

Gradual fall in the mercury level occurs at low pressure- If there is too much moisture in the air, indicates the possibility of rain

Answer is B