Question

A ideal barometer tube of negligible mass is suspended from a spring balance as shown. The mass of mercury in the tube is $m$ and atmospheric pressure is $P_0$. The cross section area of tube is $A$. The reading of spring balance is :

• A. $mg$
• B. $P_{0}A$
• C. $P_{0}A-mg$
• D. $\frac{P_{0}A+mg}{2}$

Answer 1

Answer: (A), (B)

The correct options are
A $mg$
B $P_{0}A$

As we know that spring will always measure contraction of expansion depend on the nature of force acting on it.

Now after drawing the free body diagram we find the following equation.

$Kx-mg=0$

hence the reading of spring will be $Kx=mg$

also after the action of pressure fluid inside the tube will raise some height $h$

So $P_o=\rho gh$

Therefore $\rho gh=\frac{F}{A}$

$F=P_o\times A$