Question

by what percent will the gravitational force between the two bodies be increased if their masses are increased by 50%

Answer 1

F=Gm1m2/R^2

m1`=m1+(50/100)m1=3m1/2
m2`=m1+(50/100)m2=3m2/2


F`=Gm1`m2`/R^2
F`=G ×(3m1/2)×(3m2/2)/R^2
F`=G ×3/2 ×m1 × 3/2 ×m2\R^2
F`=G×9/4 ×m1×m2/R^2
F`=9/4×(Gm1m2/R^2)
F`=9/4×F

AS F WAS Gm1m2/R^2

so now % increase= change/original ×100
i.e (F`-F)/F×100
so,(9F/4 -F)/F×100
% increase =5F/4/F×100
% increase =5/4 ×100
% increase =125%

Hence if the mass is increased by50% the force of gravitation between the 2 objects will increase by 125%


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