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Three equal masses of 1 kg each are plac...

Three equal masses of 1 kg each are placed at the vertices of an equilateral triangle PQR and a mass of 2 kg is placed at the centroid O of the triangle which is at a distance of `sqrt(2)m` from each of the vertices of the triangle. The force, in newton, acting on the mass of 2 kg is :

A

2

B

`sqrt2`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
D

Here `OP = OQ = OR = sqrt2 m`
The gravitational force on mass 2 kg at O due to mass 1 kg at P is
` F_(OP) = (G xx 2 xx 1)/((sqrt2)^2) ` = G along OP
The gravitational force on mass 2 kg at due to mass 1 kg at Q is
` F_(OQ) = (G xx 2 xx 1)/((sqrt2)^2) = ` G along OQ
The gravitational force on mass 2 kg at O due to mass 1 kg at R is
`F_(OR )= (Gxx2xx1)/((sqrt2)^2)` = G along OR
Resolving forces `F_(OQ)` and `F_(OR)` into its rectangular components. `F_(OQ)cos30^@` and `F_(OR) cos30^@` which are equal in magnitude and acting in opposite directions, cancel out each other. The resultant force on the mass 2 kg at O
`= F_(OP) - (F_(OQ) sin 30^@ + F_(OR) sin 30^@)`
` = G - (G xx 1/2 + G xx 1/2) = 0N`
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