Properties of Matter and Their Measurement - Concept of Mass and Weight

1. Mass: It is the amount of matter in an object. It is related to inertia, which is the resistance of an object to change its state (whether at rest or moving). According to Newton’s first law, it is the measure of the inertia of an object. The greater the mass, the greater the inertia.

• Mass is a scalar quantity, meaning it only has magnitude, not direction. Mass does not change from one place to another; it stays the same everywhere.
• The SI unit of mass is kg. When using a two-pan balance in a shop, we are comparing the mass of two objects.

2. Weight: It is the gravitational force that the Earth exerts on an object. It depends on the mass of the object and gravity. Its S.I. unit is Newton.

• Weight is a vector quantity, meaning it has both magnitude and direction (towards the Earth’s centre).
• Weight can change from place to place, depending on the strength of gravity (for example, at different heights or on other planets). What we commonly measure in grams or kilograms is actually mass, not weight.

W = F = m × g .......( `g = (GM)/(R^2)`)

The weight of an object can change from one place to another, from one planet to another.

The weight of an object on the moon is given by the formula.

`"W"_"m" ="GM"_"m" xx "m"/"R"_"m"^2`

• Wm= weight of an object on moon
• Mm= mass of the moon = 7.36 × 10²²
• Rm= radius of the moon = 1.74 × 10⁶
• G = Universal Gravitational Constant = 6.67 × 10⁻¹¹ Nm²/kg²
• m = Mass of the object

Substituting the values:

`therefore`  `"W"_"m" = (6.67 × 10⁻¹¹ xx 7.36 xx 10^22 xx"m")/((1.74 xx 10^6"m")^2)`

`"W"_"m" = 2.431 xx 10^10 "Gm"`

Similarly, the weight of the object on Earth is:

`"W"_"e" = 1.474 xx 10^11 "Gm"`

Taking the ratio:

`therefore` `"W"_"m"/"W"_"e" = ("Weight of object on Moon")/("Weight of object on Earth") = (2.431xx10^10"Gm")/(1.474 xx 10^11"Gm")= 1/6`

`therefore` Weight of an object on the moon is `1/6`th the weight of an object on the earth.