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For a two-particle system with total mass M and separated by some distance d, if one of the particles has mass m, what would be the ratio of the masses m/M so that the gravitational force between two particles is maximum?
  • a)
    1 : 1
  • b)
    1 : 2
  • c)
    1 : 3
  • d)
    2 : 3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
For a two-particle system with total mass M and separated by some dist...
Gravitational Force between Two Particles

Gravitational force between two particles is given by the formula:

F = G(m1m2)/d^2

where F is the force of attraction, m1 and m2 are the masses of the particles, d is the distance between them, and G is the universal gravitational constant.

Maximizing Gravitational Force

To maximize the gravitational force between two particles, we need to maximize the product of their masses. However, since the total mass of the system is constant (M), we need to find the ratio of the masses that maximizes the product.

Let the masses of the particles be m and M-m, where M is the total mass of the system. Then, the product of the masses is:

m(M-m) = -m^2 + mM

This is a quadratic function with a maximum value when m = M/2. Therefore, the ratio of the masses that maximizes the gravitational force is:

m/M = 1/2

Thus, the correct answer is option B, 1:2.
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For a two-particle system with total mass M and separated by some dist...
By the law of gravitation,

This is our required solution.
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