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Infinite number of spheres , each of mas...

Infinite number of spheres , each of mass m are placed on the X- axis at distance 1,2,4,8,16, … meter from origin . The magnitide of the gravitational field at the origin is

A

`2/3`Gm

B

`4/3`Gm

C

Gm

D

6Gm

Text Solution

Verified by Experts

The correct Answer is:
B
F= `G(1xxm)/1^2 +G(1xxm)/2^2 +…`
`Gm[1+1/4+1/16 +......]`
= `Gm[1/(1-1/4)]` `[therefore s_infty =a/(1-r)]`
`therefore F= 4/3 Gm`
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Knowledge Check

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