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

Answer

B

Explanation

In the semicircle, we can consider a small element `dtheta`
then mass of `R/dtheta=(M/L)Rdtheta`
dF=(Gmrdthetam)/(LR^2)`
dF_1=2dF`
`since =(2GMm)/(LR) sintheta d theta `:. F=int_0^(pi/2) (-2GMm)/(LR) sintheta d theta`
=(-2GMm)/(LR) (-1)`
`(2GMm)/(LR)=(2GMm)/(LL/pi)`
=(2piGMm)/L^2`