Two objects of masses m1 and m2, when separated by a
distance d, exerts a force F on each other. What happens when
(i) value of mass of first object is doubled?
(ii) Masses are brought closer so that distance between them becomes
d/2?
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(i)According to universal law of gravitation
F=(G*m1*m2)/R^2
Here m 1 is doubled
So,
F=(G*2m1*m2)/R^2
F=2*(G*m1*m2)/R^2
F=2F
Hence if the value of mass of first object is doubled then its force will also be doubled
(ii)F=(G*m1*m2)/(R/2)^2
F=(G*m1*m2)/R/4
F=1/4(G*m1*m2)/R^2
F=1/4F
F=(G*m1*m2)/R^2
Here m 1 is doubled
So,
F=(G*2m1*m2)/R^2
F=2*(G*m1*m2)/R^2
F=2F
Hence if the value of mass of first object is doubled then its force will also be doubled
(ii)F=(G*m1*m2)/(R/2)^2
F=(G*m1*m2)/R/4
F=1/4(G*m1*m2)/R^2
F=1/4F
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