A semicircular wire hs a length L and mass M. A paricle of mass m is placed at the centre of the circle. Find the gravitational attraction on the particle due to the wire.

Options

A. `(GM)/(l^(2))` along x- axis
B. `(GM)/(pi l^(2))` along y-axis
C. `(2 pi GM)/(l^(2))` along x-axis
D. `(2 pi GM)/(l^(2))` along y-axis

Answer

D

Explanation

`E_("net") = int_(0)^(pi) dE sin theta`

`= int_(0)^(pi) (G.dM)/(R^(2)) sin theta`
`= int _(0)^(pi) (G((M)/(pi) d theta))/(R^(2)) sin theta`
`= (2GM)/(pi R^(2)) = (2 G pi M)/(l^(2))`
`l = pi R`
`:. R = (l)/(pi)`