Question

An object of mass "M" is divided into two parts which are placed at a distance "d" . If gravitational force of attraction is maximum between parts then find the ratio of mass of both parts??

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Answer 1

SOLUTION

Total mass =M

Mass of one part = m

Mass of other part = M-m

Distance between the particle =D

For force to be maximum

df/dm=0

f=G(m)(M-m)/D²

f=G/D²(Mm - m²)

f=G/D²(Mm) - G/D²(m²)

Differentiate it with respect to m

df/dm=(G/D²)dMm/dm - (G/D²)dm²/dm

df/dm=G/D²(M - 2m)

FOR MAX. df/dm=0

0 = G/D² (M - 2m)

M = 2m

HENCE FOR MAX FORCE THE MASS SHOULD BE DIVIDED INTO TWO EQUAL PARTS.

Differentials.....

d(m²)/dm = 2m

d(Mm)/dm = M

Answer 2

Answer:

What is the ratio of (m/M) which maximises the gravitational force between the parts ? Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. For F to be maximum, dF/dm=0 as M & r are constants. So, the force will be maximum when the parts are

equal.

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