Question

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

Answer 1

Hint: If the density of a substance is known, its weight can be estimated by assuming some volume. It can also be found if the volume of the substance is given.

Complete step by step answer:
The density of a substance is defined as its mass per unit volume. Mathematically, it is represented as:
\[\rho = \dfrac{m}{V}\]
Density is loosely defined as its weight per unit volume, although this is scientifically inaccurate, this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration.
In the given question, we will need to investigate each option individually:
\[1{m^3}\] of water
The density of water is equal to 1000 \[\dfrac{{kg}}{{{m^3}}}\]
The given value of volume is equal to \[1{m^3}\].
Hence,
Mass of water = \[\rho \times V\]
          = 1000 $\times$ 1
          = 1000 kg

A normal adult man
An average adult man weighs around 65 kg. This is definitely lesser than what obtained in part (A).

10 L of Hg
The density of mercury is equal to 13.6 \[\dfrac{g}{{mL}}\]
The given volume of mercury is equal to 10L

Thus,
Mass of mercury = \[\rho \times V\]
          = 13.6 10 kg
          = 136 kg

All have the same weight
It is clearly seen that all the above options do not have the same weight.

Hence, the correct option is (A).

Note: Remember that to find the respective masses, we need to know the densities of the substances. Else, it would be very difficult to get the correct answer.