Question

Infinite number of bodies, each of mass 6kg, are situated at a distance 1m, 2m, 4m, 8m ........, from the origin on the y-axis. The resultant gravitational field intensity at the origin is ?

Answer 1

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Answer 2

hello friend...!!!

we should calculate the resultant gravitational field intensity :

⇒ we know , g = Gm / r² 

given m = 6 kg ,

g = Gm ( 1 / 1 + 1/4 + 1/16 + 1/64 ................)

here ,

1/1 + 1/4 + 1/16 + 1/64 are in GP 

S = a / 1 - r   ,  where r = 1 / 4 and a = 1

S = 1 / 1- 1/4 = 4 /3 

therefore ,

g = Gm ( 4 / 3  )

g = 6.6 x 10⁻¹¹ x 6 x 4 /3 

g = 5.2 x 10⁻¹⁰ m/s²

the resultant gravitational field intensity is 5.2 x 10⁻¹⁰ m/s².

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hope it helps...!!!