Measurement Mass Weight

Introduction

We know that everything is made up of matter and the different states of matter are solid, liquid, and gas. The mass and weight of each state of matter are not the same. That is why a precise explanation of mass and weight is necessary. It is important to understand the scientific use and difference between these concepts.

What is Mass?

The amount of matter contained in a body is known as mass. It is a constant fundamental quantity of the body that remains the same in every place.

• Ordinary weighing balances are used to measure the mass.

• Its SI unit is the kilogram (kg). It is a scalar quantity.

What is Weight?

It is the measure of the force of gravity exerted on a body. It is a vector quantity.

• Spring balances are used to measure the weight of a body.

• Weight is the measurement of a force therefore its SI unit is Newton (N) and another smaller unit is dyne.

• Weight of an object is different at a distinct place because gravity varies from place to place.

• Its formula is $\mathrm{W\:=\:mg}$. Where ‘W’ is the weight of a body, ‘m’ is the mass of a body, and ‘g’ is the acceleration due to gravity

• Weight is somehow related to mass by the above relation.

Metric Units of Mass and Weight

According to the metric system, the frequent units utilized in calculating mass are gram (g) and kilogram (kg) and weight is Newton.

• For example, The mass of a pencil weighs in grams, a watermelon and a gallon of paint weigh in kilograms, and a Hippopotamus weighs in tons.

From gram, other metric units of mass can be obtained using the standard metric system that is as follows: Milligram (mg), centigram (cg), decigram (dg), decagram (dag), hectogram (hg).

Conversion of Units

It is necessary to convert units of physical quantities according to the need because the usage of units depends on the situation, like the volume of a cube is expressed in meters (m), length of a ribbon is expressed in centimeters (cm).

• To calculate the volume of a cuboid in m, if the length is given in m, breadth is given in m, and height is given in cm, then it is required to change the height in cm to m. For the inter-conversion of units of the same quantity, it is important to understand the relationship between units.

• Relations between metric units of mass with gram are as follows −

 

Metric ton (t)	1000 kg
Kilogram (kg)	1000 g
Hectogram (hg)	100 g
Decagram (dag)	10 g
Gram	1000 mg
Decigram (dg)	$\mathrm{\frac{1}{10}\:g}$
Centigram (cg)	$\mathrm{\frac{1}{100}\:g}$
Milligram (mg)	$\mathrm{\frac{1}{1000}\:g}$

• When converting a big unit into a small unit do multiplication.

For example − To convert from kg to g, write the relation between kg and g

$$\mathrm{1\:kg\:=\:1000\:g}$$

Now, in the above relation kg is a bigger unit and g is a smaller unit then multiply the given quantity by 1000.

• When converting a small unit into a big unit, do divide.

For example − While converting from milligram to g, write the relation between g and mg

$$\mathrm{1\:g\:=\:1000\:g}$$

Now, in the above relation mg is the smaller unit and g is the bigger unit then divide the given unit by 1000.

Solved examples

Ron bought 2 tonnes of sand for the construction of a building out of which only 1100 kg of sand is used. Calculate how much sand is left.

Ans. Given − Ron bought sand = 2 tonnes

$$\mathrm{1\:ton\:=\:1000\:kg}$$

$$\mathrm{2\:tons\:=\:2\times\:1000\:kg\:=\:2000\:kg}$$

$\mathrm{sand\:used\:for\:construction\:=\;1100\:kg}$

$\mathrm{sand\:left\:unused\:=\;2000\:-\:1100\:=\:900kg}$

The body of mass 45 kg is situated on the earth. What is the weight of the body?

Ans. Given −

$\mathrm{mass\:=\:45kg}$

$\mathrm{The\:acceleration\:dur\:to\:gravity\:=\:9.8ms^{-2}}$

$$\mathrm{W\:=\:m\times\:g}$$

$$\mathrm{W\:=\:45\times\:9.8\:=\:441N}$$

Calculate the mass of a body if its weight is 80N.

Ans. Given − $\mathrm{weight\:=\:80N}$

$\mathrm{The\:acceleration\:dur\:to\:gravity\:=\:9.8ms^{-2}}$

$$\mathrm{m\:=\:\frac{W}{g}}$$

$$\mathrm{m\:=\:\frac{80}{9.8}\:=\:8.16kg}$$

Conclusion

In this tutorial, we cover the concept of measurement of the mass and weight using weighing balance and spring balance. Also, we learn how the mass and weight are calculated, correlation and dissimilarity between them.

FAQs

1. Why it is said that weight can be zero but mass cannot be zero?

Mass and weight are different in the context that mass will not be zero in any circumstance as it is the number of particles contained in an object and none of the objects will contain zero particles but weight can be zero because it is the gravitational pull on the body and in the case of free fall the body falls in the direction of gravity due to which the weight of the body becomes zero.

2. How mass is related to weight?

Mass is related to weight as the correlation between them can be obtained by using Newton's second law. If an object of mass 1kg falls from a height with acceleration due to gravity, g. Then force applied to the body is given by

$$\mathrm{F\:=\:m\times\:g}$$

$$\mathrm{F\:=\:1kg\times\:9.8ms^{-2}\:=\:9.8kgms^{2}\:=\:9.8N}$$

3. The weight of a body on the moon is one-sixth its weight on the earth. Give a reason

The mass of the moon is lesser as compared to the mass of earth due to which the moon applies less attractive force than earth on the body that is why on moon the body weighs one-sixth of the weight on earth.

4. What is relativistic mass?

In the special theory of relativity, relativistic mass is associated with the mass of the body in motion. The relativistic mass is given by

$$\mathrm{m\:=\:\gamma\:\times\:m_{0}}$$

where 𝑚𝑜 is the rest mass

𝛾 is the factor greater than one

It increases with an increase in the velocity of the body.

5. What is weightlessness?

The term weightlessness means no presence of weight. As weight is the measure of gravity it means weightlessness means the absence of gravity. During free fall there is no gravity so free fall is the condition of weightlessness. It is also called zero gravity or zero G-force.

6. Do photons have mass?

Photons are generally known as massless. Photons are the magnitude of light as they do not have mass therefore light also has no mass.

7. An object weighs less at the equator than at the poles. Give a reason.

An object weighs less at the equator than at the poles because gravitational force is less at the equator as its distance is less from the center of the earth. On the other hand, the distance between poles is more from the center of the earth due to which gravitational force is more here hence, the weight of a person is also more.