Question

Distinguish between inertial mass , gravitational mass and weight of a body.

Answer 1

 
 Gravitational mass:-It is defined by the force of gravitation, which states that there is a gravitational force between any pair of objects

Inertial mass:- It is mainly defined by Newton's law,  F = ma, which states that when a force F is applied to an object, it will accelerate proportionally, and that constant of proportion is the mass of that object. In very concrete terms, to determine the inertial mass, you apply a force of F Newtons to an object, measure the acceleration in m/s2, and F/a will give you the inertial mass m in kilograms. 

Weight of a body:-It defines weight as the force exerted on a body by gravity. expressed in the formula W = mg, where W is the weight, m the mass of the object, and g gravitational acceleration.

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Answer 2

Inertial mass:

To every particle in nature we can associate a real number with it so that the value of the number gives the measure of inertia (the amount of resistance of the particle to accelerate for a definite force applied on it) of the particle.

Using Newton's laws of motion,

mi=Fami=Fa

Gravitational mass:

(This is defined using Newton's law of universal gravitation i.e. the gravitational force between any two particle a definite distance apart is proportional the product of the gravitational masses of the two particles.) To every particle in nature we can associate a real number with it so that the value of the number gives the measure of the response of the particle to the gravitational force.

F=GmG1mG2R2F=GmG1mG2R2

All experiments carried out till date have shown that mG=mimG=mi

This is the reason why the acceleration due to gravity is independent of the inertial or gravitational mass of the particle.

mia=GmG1mG2R2mia=GmG1mG2R2

If mG1=mimG1=mi then

a=GmG2R2a=GmG2R2

That is acceleration due to gravity of the particle is independent of its inertial or gravitational mass.

the weight of an object is usually taken to be the force  on the object due to gravity
Weight is a vector  whose magnitude (a scalar quantity), often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational attraction g; thus: W = mg