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Q.

What is the separation between the two massive particles, each of mass 5 mg, if they experience a gravitational force of 6.66 dyne?

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a

5×10-8 m

b

 0.5×10-9 m

c

 5×109 m

d

5×10-9 m 

answer is D.

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Detailed Solution

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The separation between the two massive particles is  5×10-9 m.
Given,
Mass of the first object, m1=5 mg
Mass of the second object, m2=5 mg
Gravitational force, F=6.66 dyne
In SI unit, the given data can be written as
Mass of the first object, m1=5×10-6 kg
Mass of the second object, m2=5×10-6 kg
Gravitational force, F=6.66×10-5 N
We know that the gravitational force between two particles is given by the formula:
F=Gm1m2 r2
where G is the universal gravitation constant, m1 is the mass of the first object, m2 is the mass of second object and r is the distance between them.
It can also be written as
  r=G.m1m2F
On substituting the given values, we get
  r=6.66×10-11×(5×10 -6)26.66 ×10-5 
 r=5×10-9 m

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