Four particles of masses m,2m , 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the centre of the square sill be:

Options

A. zero
B. `(klambda)/R`
C. `(2klambda)/R`
D. `(kpilambda)R`

Answer

C

Explanation

As, R be the radius of the ring. Consider a small strip of length dl having charge dq lying at an angle `theta`.
`dl = Rdtheta`
Charge on dl=`lambdaRdtheta`
Force at 1C due to dl
`=(klambdaRdtheta)/(R^(2)) = (klambda)/R dtheta=dF`
We need to consider only the component `dRcostheta`, as the component `dFsintheta` will cancel out because of the symmetrical element dl.

The total force on 1 C is
`F= int_(-pi//2)^(pi//2)dFcostheta= (klambda)/Rint_(-pi//2)^(pi//2)costhetad(theta)=(klambda)/R xx 2 = (2klambda)/R`