The acceleration of a freely falling body does not depend on the mass of the body. Prove this.
Answers
Newton’s 2nd Law:
F = ma
This is an axiomatic statement and is not based on underlying proof, it just seems to be how the world works.
Accordingly, the acceleration of a body experiencing a net force is
a = F/m
This applies to any body under any force.
Uniquely under the forces, the force of gravity felt by a body depends on its mass. This means if you double the mass of a ball falling to Earth, you double the force on it.
After applying the relavant conventions and simplifications, gives us the popular
F = m . a (Eq. 1)
where F is force.
m is the mass of the body
a is the acceleration of the body
or a = F / m (Eq. 1.a)
Also the gravitational force exerted between two bodies of masses M and m is given by
F = G . M . m / r^2 (Eq. 2)
where F is gravitational force
G if universal Gravitational constant
M and m are the masses of the two bodies
r is the distance between the two bodies
for the case of free fall on earth, ‘M’ can be considered as the mass of earth and ‘m’ as the mass of the free-falling body.
Considering Eqns. 1.a and 2, the acceleration of the free falling body would be
a = ( G . M . m / r^2 ) / m. (Eq. 3)
or a = G . M . m / r^2 . m (Eq. 3.a)
a = G . M . m / r^2 / m (Eq. 3b)
m in the numerator and denominator divides to give 1.
a = G . M / r^2 (Eq. 4)
From (Eq. 4) you can see that the acceleration is independent of the mass of the free-falling body and depends on M, in this case, the mass of earth...
So bu u can say it is not depend on mass of a object....
Hope you understood..
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