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Three identical point masses, each of ma...

Three identical point masses, each of mass 1 kg lie in the x-y plane at point (0,0),(0,0.2 m) and (0.2 m, 0) The net gravitational force on the mass at the origin is

A

`1 . 67 xx 10^(-9) (hat(i) + hat(j)) N`

B

`3 . 34 xx 10^(-10) (hat(i) + hat(j))N`

C

`1 . 67 xx 10^(-9) (hat(i) - hat(j))N`

D

`3 . 34 xx 10^(-10) (hat(i) + hat(j))N`

Text Solution

Verified by Experts

The correct Answer is:
A

Let particle a lies origin, particle B and C on y and x - axis respectively
`vec(F_(AC)) = (Gm _(A) m_(B))/( r_(AB)^(2)) hat(i) = (6 . 67 xx 10^(-11) xx 1xx 1)/((0.2)^(2)) hat(i) = 1. 67 xx 10^(-6) hat(i) N ` , Similarly `vec (F_(AB)) = 1. 67 xx 10^(-9) hat(j) N`
`:.` Net force on particle A ` vec(F) = vec(F)_(AC) + vec(F)_(AB) = 1. 67 xx 10^(-9) (hat(i) + hat(j))N`
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