Two light plastic bags of negligible mass are placed 2 meters apart. Each bag contains 15 mangoes. If 10 mangoes were moved from one bag to the other, the gravitational force between the two bags would

[1] increase to 3/2 the original value.

[2] decrease to 2/5 the original value.

[3] increase to 5/3 the original value.

[4] decrease to 5/9 the original value.

[5] not change

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From Newton's law of gravitational interaction, we know the gravitational force between two objects in the surface of Earth,

`F=(GMm)/r^2`

(where G is a universal constant known as gravitational constant, M and m are the masses of the two objects and r, the distance between them)

Suppose each mango weighs x kg.

The ratio of gravitational forces in the two cases described above would be:

`F_1/F_2=((G*((15x)/g)*((15x)/g))/2^2)/((G*((25x)/g)*((5x)/g))/2^2)`

`=225/125`

`=9/5`

Therefore, `F_2=5/9 F_1 `

Thus the correct answer is at option 4).

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