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 :

Options

A. 2
B. `sqrt2`
C. 1
D. Zero

Answer

D

Explanation

Here, OP=OQ=OR=`sqrt2`m
The gravitational force on mass 2 kg at O due to mass
1kg at P is `F_(OP)=(Gxx2xx1)/((sqrt2)^2)=G` along OP
The gravitational force on mass 2 kg at O due to mass
1kg at Q is `F_(OQ)=(Gxx2xx1)/((sqrt2)^2)=G` along OQ
The gravitational force on mass 2 kg at O due to mass
1kg at R is `F_(OR)=(Gxx2xx1)/((sqrt2)^2)=G` along OR
Resolve forces `F_(OQ)` and `F_(OR)` into two rectangular components.
`F_(OQ)cos30^(@)` and `F_(OR)cos30^(@)` are equal in magnitude of equal and opposite direction.
`=F_(OP)-(F_(OQ)sin30^(@)+F_(OR)sin30^(@))`
`=G-(Gxx1/2+Gxx1/2)=G-G=Zero N`