A tube of length h (which is wide enough so that surface tension effects can be neglected) filled with air at atmosphere pressure and closed at one end. Now tube is lowered in a tank of mercury to a depth h as shown. It is seen that mercury rises a distance x into the tube. If the mercury barometer also reads h, then

Options

A. `h(h-x)=h^(2)`
B. `(2h-x)(h-x)=h^(2)`
C. `(2h-x)(h+x)=h^(2)`
D. `(2h)(h-x)=h^(2)`

Answer

B

Explanation

For air in tube, `P_(0)ha=P(h-x)aimpliesP'=(P_(0)h)/(h-x)=(h^(2)deltag)/(h-x)" "("Given":P_(0)=hdeltag)`
At bottom most point, `P_(0)+deltagh=P'+"deltagximplies2deltagh"=(deltagh^(2))/(h-x)+`deltagximplies`(2h-x)(h-x)=h^(2)`