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Question

Why is gravitational mass equal to inertial mass?


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Solution

Step 1: Let us suppose

Calculating the ratio of gravitational force

Consider bodies A,A*with gravitational mass Mg,Mg*.

Let the bodies be kept in the gravitational field of the earth of Mass M and distance R.

The gravitational force on both the bodies is:

F=GMMgR2,F*=GMMg*R2

The ratio of force is, FF*=MgMg*

Step 2: Calculating the ratio of inertial force

Similarly consider bodies A,A* with inertial mass Mi,Mi*

The force on these bodies in influence to acceleration due to gravity is

F=Mig,F*=Mi*g

The ratio of force is, FF*=MiMi*

Step 3: Calculating the relation between inertial and gravitational mass

MgMg*=MiMi*

Therefore, this implies that gravitational mass is proportional to inertial mass ie MgαMi.

Hence both gravitational and inertial mass are the same.


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