Physics

Classical Mechanics Level 2

If the distance between two objects is halved and their masses are doubled, then the gravitational force between them will become

No change 2 times 4 times 16 times

Ankit Vijay by Ankit Vijay , 22, India

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1 solution

Anoir Trabelsi
Jun 3, 2014

U s i n g N e w t o n ′ s l a w o f g r a v i t a t i o n w e h a v e : F = G m M r 2 w h e n t h e t w o m a s s e s a r e d o u b l e d a n d t h e d i s t a n c e i s h a l v e d w e h a v e : F ′ = G 2 m . 2 M ( 1 2 r ) ² = G . 4 m M 1 4 r ² = 16 G m M r ² = 16 F ∴ F ′ = 16 F Using\quad Newton's\quad law\quad of\quad gravitation\quad we\quad have\quad :\\ F\quad =\quad G\frac { mM }{ { r }^{ 2 } } \\ when\quad the\quad two\quad masses\quad are\quad doubled\quad and\quad the\quad distance\\ is\quad halved\quad we\quad have\quad :\quad \\ F'\quad =\quad G\frac { 2m.2M }{ (\frac { 1 }{ 2 } r)² } \quad =\quad G.\frac { 4mM }{ \frac { 1 }{ 4 } r² } =\quad 16\quad G\frac { mM }{ r² } \quad =\quad 16\quad F\quad \\ \\ \therefore \quad \boxed { F'\quad =\quad 16\quad F\quad }

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can you edit your problem so that it say both masses are doubled, bit misleading even though there is not choice 8 as the answer @anik

Mardokay Mosazghi - 7 years ago

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