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...

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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