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# Convert $1$ mm of Hg into Pa. take density of Hg $= 13.6 \times {10^3}kg{m^{ - 3}}$ and g $= 9.8m{s^{ - 2}}$. Let it be x Pa. find$[\dfrac{x}{{40}}]$. Where $[]$ is a step function. A. $3$B. $4$C. $5$D. $6$

Last updated date: 09th Aug 2024
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Hint: To solve this question we have to know about pressure and the formula of pressure. So, we know that pressure is the perpendicular force per unit area or the stress at a point. The S.I unit of pressure is pascal. We know that one pascal is equal to one newton per square meter. We also know that the atmospheric pressure is almost equal to one hundred thousand which means one lakh Pascal. We also know that pressure is equal to the multiplication of density height and the gravitational force. In this question we are going to use this formula only.

we know that, P$= \rho gh$. Here g is equal to the gravitation. $\rho$ is equal to the density. And P is equal to the pressure.
$\rho = 13.6 \times {10^3}kg{m^{ - 3}}$
$\Rightarrow g = 9.8m{s^{ - 2}}$
$\Rightarrow h = {10^{ - 3}}m$
$P = 13.6 \times {10^3}kg{m^{ - 3}} \times 9.8m{s^{ - 2}} \times {10^{ - 3}}m \\ \Rightarrow P = 133.28kg{m^{ - 1}}{s^{ - 2}} \\$
So, x is equal to $133.28$. Therefore,
$\dfrac{x}{{40}} = 3.332 \\ \therefore[\dfrac{x}{{40}}] = 3 \\$