Question

The maximum value of water pressure in the box in which water is filled upto a height of $4m$ is equal to (atmospheric pressure $={10}^{5}N/m^2,$ density of water $=1000kg/m^3$, $g=10m/s^2$)

• A. 1.4 MPa
• B. 0.14 MPa
• C. 0.104 MPa
• D. 0.014 MPa

Answer 1

Answer: (C)

0.104 MPa

The maximum pressure would be at the bottom of the box. The pressure $P,$ at depth below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount $\rho gh$.

Given:

Atmospheric pressure $P_a={10}^{5}N/m^2$

Density of water $\rho =1000kg/m^3$

Height of liquid $h=4m$

So, maximum pressure in the box,

$P_{bottom}=P_a+\rho gh$

$\Rightarrow P_{bottom}={10}^5+({10}^3\times 10\times 4)N/m^2$

$=[{10}^5+(4\times {10}^4\left)\right]Pa$ ($\because 1N/m{/}^2=1Pa$)

$=[{10}^5+(4\times {10}^4\left)\right]\times {10}^{-6}MPa$ ($\because 1Pa={10}^{-6}Mpa$)

$=[0.1+0.04]MPa=0.14MPa$

Thus, option (B) is correct.