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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: 23rd Feb 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.
Here according to the question,
$\rho = 13.6 \times {10^3}kg{m^{ - 3}}$
$\Rightarrow g = 9.8m{s^{ - 2}}$
$\Rightarrow h = {10^{ - 3}}m$
So, after putting these values we will get,
$P = 13.6 \times {10^3}kg{m^{ - 3}} \times 9.8m{s^{ - 2}} \times {10^{ - 3}}m \\ \Rightarrow P = 133.28kg{m^{ - 1}}{s^{ - 2}} \\$
So, x is equal to $133.28$. Therefore,
$\dfrac{x}{{40}} = 3.332 \\ \therefore[\dfrac{x}{{40}}] = 3 \\$
Hence, option A is the right answer.

Note: We have to keep it in our mind that we have to calculate all these units in the same unit. We calculated here in Pascal which is the S.I unit of pressure. So, we have to calculate the things in the S.I unit. Otherwise the calculation will not happen correctly. We have to keep that in our mind properly to solve these kinds of questions.