Gravitation

JEE Main level, single correct, medium

12 of 223

Question 12 of 223

Two objects of equal masses placed at certain distance from each other attracts each other with a force of FF. If one-third mass of one object is transferred to the other object, then the new force will be

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Answer: (C) 89F\dfrac{8}{9}F

The gravitational force between particles is given by, F=Gm1m2r2F=\dfrac{G{m}_{1}{m}_{2}}{{r}^{2}}
∵F=Gm2r2∵F=\dfrac{G{m}^{2}}{{r}^{2}}
When one-third mass is transferred to other object
m1=2m3,m2=4m3{m}_{1}=\dfrac{2m}{3},{m}_{2}=\dfrac{4m}{3}
F2=8Gm29r2{F}_{2}=\dfrac{8G{m}^{2}}{9{r}^{2}}
⇒F2=89F\Rightarrow {F}_{2}=\dfrac{8}{9}F

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