Barometer of Mercury: Weight or Pressure?

[adjacent]

Homework Statement

Some websites say that mercury level balances because the weight of the mercury column gets equal to the wight of atmosphere.Is it not the pressure of the mercury column equal to the pressure of the atmosphere.
I say this because if the mercury column is wide,the weight of the mercury column can get equal to atm at a lower height.
Which one is right

Homework Equations

mercury column height is 76cm

The Attempt at a Solution

 

[Sunil Simha]

You agree that the pressure of the mercury at the interface of mercury and air is P_atm right?

The upward force on the column due to this pressure is P_atmA (where A is the cross section area). The downward force on it is its weight which is ρghA.

Since they balance, ρghA=P_atmA
and therefore ρgh=P_atm. This also means that the pressures balance.

So both are right.

[edit]: as you can see, the cross section area has no significance here as long as it is uniform.

 

[adjacent]

if the pressure of the mercury column equals then both the barometers should have the same height regardless of the width of the mercury column
but if weight is to be equal,a column wide can hold more amount of mercury with less height)meaning pressure will be less) and a column narrow can hold the same amount of mercury but needing more height (meaning pressure is more)
as P=ρgh
So the two columns have different pressures but equal weight
I don't understand this

 

[adjacent]

The upward force on the column due to this pressure is P_atmA (where A is the cross section area). The downward force on it is its weight which is ρghA.

Since they balance, ρghA=P_atmA
and therefore ρgh=P_atm. This also means that the pressures balance.

The two As cannot be same because first A is the cross-sectional area the area of the mercury column cannot be used as that therefore two As cannot cancel
Am I right?

 

[SteamKing]

But the two columns have the SAME pressure at the base. Force = pressure * area. If you increase the area and pressure remains constant, then the FORCE must increase.

 

[adjacent]

According to you (SteamKing)if the pressure is constant(mercury column with same height)And as area increases more mercury can occupy that area and the force increase
I was asking about that,is that the pressure which remains constant or the force
By the way is force necessary for being in balance?
What is necessary here is the pressure.Am I right?So force is always not necessary for being in balance,Right?

 

[adjacent]

I was not thinking about equation but the image I think that is why I was Confused

 

[Sunil Simha]

By the way is force necessary for being in balance?
What is necessary here is the pressure.Am I right?So force is always not necessary for being in balance,Right?

Of course force is necessary to be balanced. Else the column would accelerate. Weight of the mercury column increases with increase in area but so does the force due to the external pressure. And they both increase by the same factor ( namely A) and thus always balance each other.

 

[adjacent]

I found sunil simha to be right after thinking about it.Thank you sunil