Chapter 19, Problem 11A

What is the mass of 1 liter of water in kilograms? What is its weight in newtons?

To determine

Mass of water in kilo-gram and weight in newton.

Answer to Problem 11A

The mass of water is $m=1\text{kg}$ and it’s weight is $F_g=10\text{N}$ .

Explanation of Solution

Given:

Mass of metal, $m=4.7\text{kg}$

Volume of water, $V=1\text{liter}$

Formula Used:

Density is given as,

  $\rho =\frac{m}{V}$

Where, $\rho$ is density, $m$ is mass and $V$ is volume.

And the weight is given as,

  $F_g=mg$

Where, $m$ is mass and $g$ is acceleration due to gravity.

Calculation:

As density of water is $\rho =1000{\text{kg/m}}^3$

And $1{\text{m}}^3=1000\text{liter}$

So, $1\text{liter}={10}^{-3}{\text{m}}^3$

Therefore, the mass of water is

  $\begin{array}{l}m=\rho V\\ =1000\times {10}^{-3}\\ \Rightarrow m=1\text{kg}\end{array}$

And taking $g=10{\text{m/s}}^2$

The weight of water is,

  $\begin{array}{l}{F}_g=mg\\ =1\times 10{\text{kg-m/s}}^2\\ \Rightarrow F_g=10\text{N}\end{array}$

Conclusion:

Therefore, the mass of water is $m=1\text{kg}$ and it’s weight is $F_g=10\text{N}$ .