(a) Calculate the height of a water column which will exert on its base the same pressure as the 70 cm column of mercury. Density of mercury is 13.6 g $c m^{- 3}$ .

(b) Will the height of the water column in part (a) change if the cross section of the water column is made wider ?

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Solution

$left parenthesis a right parenthesisG i v e n space comma space d e n s i t y space o f space m e r c u r y space rho apostrophe equals 13.6 space g c m to the power of negative 3 end exponentH e i g h t space o f space m e r c u r y space c o l o u m n space comma h apostrophe equals 70 space c mA c c e l e r a t i o n space d u e space t o space g r a v i t y comma g equals 9.8 m s to the power of negative 2 end exponentl e t space h space b e space t h e space h e i g h t space o f space t h e space w a t e r space c o l o u m n spaceD e n s i t y space o f space w a t e r space comma rho equals 1 space g c m to the power of negative 3 end exponentG i v e n space p r e s s u r e space e x e e r t e d space b y space m e r c u r y space c o l o u m n equals p r e s s u r e space e x e r t e d space b y space space w a t e r space c o l o u m no r space h apostrophe rho apostrophe g equals h rho go r space comma space h equals fraction numerator h apostrophe rho apostrophe over denominator rho end fraction equals fraction numerator 70 cross times 13.6 over denominator 1 end fraction equals 952 space c m equals 95.2 space mleft parenthesis b right parenthesisN o comma space t h e space h e i g h t space o f space t h e space w a t e r space c o l o u m n space s h a l l space n o t space c h a n g e$

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