Two particles are placed at some distance from each other. If, keeping the distance between them unchanged, the mass of each of the two particles is doubled, the value of gravitational force between them will become :
(a) $\frac{1}{4}$ times
(b) $\frac{1}{2}$ times
(c) 4 times
(d) 2 times

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Solution

$w e space k n o w space t h a t comma a c c o r d i n g space t o space g r a v i t a t i o n a l space f o r c e space space space space space space space space space space space F equals fraction numerator G M m over denominator r squared end fraction w h e r e F equals f o r c e space b e t w e e n space 2 space m a s s M equals f i r s t space m a s s m equals s e c o n d space m a s s G equals g r a v i t a t i o n a l space c o n s tan t r equals d i s tan c e space b e t w e e n space 2 space m a s s a c c o r d i n g space t o space t h e space q u e s t i o n F to the power of apostrophe equals n e w space f o r c e space w h e n space m a s s space i s space d o u b l e d i f space m a s s space o f space e a c h space p a r t i c l e space i s space d o u b l e d i e space space space space space space space space space space space space space space space space space space space space M equals 2 M space space space a n d space m equals 2 m t h e s e space v a l u e s space p u t space i n space e q u a t i o n w e space g e t F to the power of apostrophe equals fraction numerator G open parentheses 2 M close parentheses open parentheses 2 m close parentheses over denominator r squared end fraction F to the power of apostrophe equals 4 fraction numerator G M m over denominator r squared end fraction F to the power of apostrophe equals 4 F$
option c is correct

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Q. Question 9
Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be

(a)

\frac{1}{4} t i m e s

(b)

4 t i m e s

(c)

\frac{1}{2} t i m e s

(d) Unchanged

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(a) $x / 4$
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Two particles are placed at some distance from each other. If, keeping the distance between them unchanged, the mass of each of the two particles is doubled, the value of gravitational force between them will become : (a) 14 times (b) 12 times (c) 4 times (d) 2 times

option c is correct

Two particles are placed at some distance from each other. If, keeping the distance between them unchanged, the mass of each of the two particles is doubled, the value of gravitational force between them will become :
(a) $\frac{1}{4}$ times
(b) $\frac{1}{2}$ times
(c) 4 times
(d) 2 times