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प्रश्न
- 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 cm-3.
- 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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उत्तर
(a) As we know,
Pressure due to water column of height h = hρg
Pressure due to water column = Pressure due to mercury column
Hence, hw ρw g = hm ρm g
Given, hm = 70 cm, ρm = 13.6 g cm-3, ρw = 1 g cm-3
From the above formula, we get,
hw = `("h"_"m" rho_"m")/rho_"m"`
Substituting the values, we get,
hw = `(70 xx 13.6)/1`
hw = 952 cm
∴ hw = `952/100` = 9.52 m
Hence, height of a water column = 9.52 m
(b) No, if the cross-section of the water column is made wider, the height of the water column will be unaffected.
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