# Mass Calculator

## What is Mass

• The term mass is used for how much matter an object under consideration has. Mass is the measure of the inertia of an object
• The mass contained in a body is denoted by letter M or m
• Mass is a scalar quantity as it has magnitude only but no direction
• The SI unit of mass is Kilogram (Kg).
Mass can be calculated using Various ways
Using Density
$\text{Mass} = \text{Volume} \times \text{density}$
or
$m= V \times \rho$
Where
m -> Mass of the Body
V-> Volume of the body
$\rho$ -> Density of the body
Using Newton's Second Law
$\text{Mass}= \frac {\text{force}}{\text{acceleration}}$
or
$m = \frac {F}{a}$
where
F -> Force on the body
a -> Acceleration of the Body
m -> mass of the body
Using Weight
$W= mg$
Where
W -> Weight of the body
m -> mass of the body
g -> Acceleration due to gravity

## Mass Calculator using Density Formula

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.

Formula used
$m=V \times \rho$

### Mass Calculator

Example of Few questions where you can use this Mass Calculator using Density Formula
Question 1
Calculate the Mass of the body having volume 1000m3 and density 25 kg/m3
Solution
Given ,m=?, V=1000m3, $\rho =25 \ kg/m^3$
Mass is given by the formula
$m= V \times \rho = 1000 \times 25 = 25000 \ kg$

Question 2
A object has density as $20 \ kg/m^3$. The mass is 2 kg. Find the Volume.
Given , m= 2 kg, V=?, $\rho=20 \ kg/m^3$
Density is given by
$\rho = \frac {mass}{Volume} = \frac {m}{V}$
Rearranging this $V = \frac {m}{\rho} = \frac {2}{20} = .1 \ m^3$

## How the Mass Calculator works

1. If volume and density are given
$m = \rho \times V$
2. If mass and volume given
$\rho =\frac {m}{V}$
3. If mass and density are given
$V= \frac {m}{ \rho}$

## Mass Calculator using F=ma

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.

Formula used
$m=\frac {F}{a}$

### Mass Calculator

Example of Few questions where you can use this Mass Calculator using F=ma
Question 1
A Body is acted by the force of 8 N and it start moving with the acceleration 2 m/s2.Find the mass of the body
Solution
m = ?, a =2 m/s2, F=8N
Now as per Mass formula
$m= \frac {F}{a} = \frac {8}{2}= 4 \ kg$

Question 2
A Force of 20 N acts on the body of mass 10 kg.Find the acceleration of the body.
Solution
m = 10 kg, a =? , F=20 N
Now as per Newton second law formula
$f=ma$
or
$a = \frac {F}{m} = \frac {20}{10} = 2 \ m/s^2$

## How the Mass Calculator using Newton second lawworks

1. If acceleration and force are given, mass is calculated as
$m = \frac {F}{a}$
2. If mass and acceleration are given, Force is calculated as
$F= ma$
3. If mass and force are given, acceleration is calculated as
$a= \frac {F}{m}$

## Mass Calculator using Weight Formula

Note
• Enter the values of the two known variables in the text boxes
• Leave the text box empty for the variable you want to solve for
• Click on the calculate button.

Formula used
$m=\frac {W}{g}$

### Mass Calculator

Example of Few questions where you can use this Mass Calculator using weight Formula
Question 1
A person has weight has 686 N on the surface of the earth .Acceleration due to gravity at that point is 9.8 m/s2.Find the mass of the body
Solution
m = ?, g =9.8 m/s2, W=686 N
Now as per Mass formula
$m= \frac {W}{g} = \frac {686}{9.8}= 76 \ kg$

Question 2
The gravity of Jupiter is about 26 m/s2. What would be the weight of a probe of mass 1000 kg at Jupiter's surface?.
Solution
m = 100 kg, g =26 m/s2 , W=?
Now as Weight formula
$W=mg = 100 \times 26 = 2600 \ N$

## How the Mass Calculator using Weight Formula

1. If acceleration due to gravity and Weight are given, mass is calculated as
$m = \frac {W}{g}$
2. If mass and acceleration due to gravity are given, Weight is calculated as
$W= mg$
3. If mass and Weight are given, acceleration due to gravity is calculated as
$g= \frac {W}{m}$