Two bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M each are placed R/2 a distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies i

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Q: (NDA-II/2019)
Two bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M each are placed R/2 a distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies in the second system will be

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,26,27,26,3,19,5

keywords: 

{'gravitational force': [0, 0, 0, 6], 'second system': [0, 0, 0, 1], 'mass': [0, 0, 2, 3], 'first system': [0, 0, 1, 1], 'distance': [0, 3, 3, 3], 'system': [8, 3, 7, 23], 'bodies': [0, 0, 3, 10]}

In the given question, we have two systems. In the first system, there are two bodies of mass M each, placed R distance apart. In the second system, there are two bodies of mass 2M each, placed R/2 distance apart.

The gravitational force between two bodies is given by the equation F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between the two bodies.

Now, let`s analyze each option:

Option 1: 16 F

This option suggests that the gravitational force in the second system is 16 times the force in the first system. This is the correct answer because the gravitational force is directly proportional to the product of the masses (m1 * m2). In the second system, the masses are 2M and 2M, which is 4 times the mass in the first system. Therefore, the gravitational force in the second system will be 16 times the force in the first system.

Option 2: 1 F

This option suggests that the gravitational force in the second system is equal to the force in the first system.