Question

42. For the given figure ratio of pressure at A and B
will be (p
1000 kg/m3, P.
= 105
105 pa) :-
10m
АР
РА
PR
?
20m
22
B
PLUD MECHANCSENERCISES
(1) 1/2
(2) 1/4
(3) 1/3
(4) 2/3​

Answer 1

Answer:

1/2 is the right answer

Answer 2

Answer:

The correct answer is (3) 1/3

Explanation:

Given:

A figure of a setup where ρ is 1000 Kg/m^3 and P(atm) =10^5 pa

To find:

The ratio of pressure at points A and B.

Solution:

We know that according to the hydrostatic pressure equation, the pressure exerted by a column of liquid of height h and density ρ is given by the expression:

Pressure p = ρgh, where

g = acceleration due to gravity

Now, according to the question, for point A:

The height of the column of water at point A = 10 m

The pressure exerted by the column of the liquid at point A = ρgh

=> Pressure exerted by the column of the liquid at point A = ρ × g × (10 m)

=> Pressure exerted by the column of the liquid at point A = 10ρg pa

Therefore, the pressure exerted by the column of the liquid at point A = (10ρg) pa ............... (i)

Similarly, for the point B:

The height of the column of water at point B => 10 m + 20 m = 30 m

Pressure exerted by the column of the liquid at point B = ρgh

=> Pressure exerted by the column of the liquid at point B = ρ × g × (30 m)

=> Pressure exerted by the column of the liquid at point B = 30ρg pa

Therefore, the pressure exerted by the column of the liquid at point B = (30ρg) pa .............. (ii)

Now, the ratio of pressure at points A and B = (the pressure exerted by the column of the liquid at point A) / (the pressure exerted by the column of the liquid at point B)

Therefore, Pa / Pb => (10ρg) pa/(30ρg) pa = 1/3

Hence, the ratio of pressure at points A and B is 1/3. Therefore, the correct option is (3) Pa / Pb = 1/3

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