Question

Which has the highest weight?
A. \[1{m^3}\] water
B. A normal adult man
C. 10 litre of Hg
D. All have the same weight

Answer 1

Hint: Density, Volume, and mass of a substance are related to each other as:
\[Density = \dfrac{{Mass}}{{Volume}}\]
Mass and density are very commonly used physical properties in the field of science and technology. Mass is defined as the measure of matter in an object. It's S.I unit is grams and it is not affected by gravity. Hence an object will have the same mass everywhere. Weight is the force of gravity that acts upon an object’s mass and in the absence of gravity objects have no weight.
\[Weight = mg\]
M is the mass of object
g represents Acceleration due to gravity (\[9.8m/{s^2}\])

Complete step by step answer:
Let us calculate the weight for all the options one by one. First of all, we will calculate the mass of a substance from the given values and then multiply it by the acceleration due to gravity on earth to calculate its weight and then compare their values.

\[1{m^3}\] water
Here, \[Volume = 1{m^3}\]
\[Density(water) = 1000kg/{m^3}\]
\[Mass = Volume \times Density\]
\[ \Rightarrow Mass = 1 \times 1000 = 1000kg\]
We know that \[Weight = mg\]
\[Weight = 1000 \times 9.8\]
\[Weight = 9800Newton\]
Hence the weight of \[1{m^3}\] water is 9800 newtons.

A normal adult man
Mass of normal adult man is \[75kg\] (based on assumption)
\[Weight = 75 \times 9.8\]
\[Weight = 735Newton\]
10 litre of Hg
\[Volume = 10L = 10 \times 0.001\]
\[Volume = 0.010{m^3}\]
\[d = 13600kg/{m^3}\]
\[Mass = Volume \times Density\]
\[ \Rightarrow Mass = 0.010 \times 13600\]
\[ \Rightarrow Mass = 13.6kg\]
\[Weight = Mass \times 9.8\]
\[Weight = 13.6 \times 9.8\]
\[ \Rightarrow Weight = 133.28newton\]`
(Initially we have changed the units of volume in this calculation then calculated the weight from mass)
On comparing all the options, we can see that \[1{m^3}\] water has the highest weight.

So, the correct answer is Option A.

Note: Mass and weight are different physical quantities.Mass remains the same everywhere whereas weight depends upon the acceleration due to gravity as weight is a force.The S.I unit of weight is the same as the force which is Newtons (N).