A long non-conducting, massless rod of length L pivoted at its centre and balanced with a weight w at a distance x from the lefrt end. At the left and right ends fo the rod are attached small conducting sphers with positive charfges q and `2q` respectively. A distance h directly beneath each of these spheres is a fixed sphere with positive charge Q.
(a) Find the distance x where the rod is horizontal and balanced.b. What valueshold h have so that the rod exerts no vertical force on the bearing when the rod is horizontal and balanced?

Answer

B, C, D

Explanation

a. Net torque on the rod about O=0`
`1/(4piepsilon_0)(Q(2q))/h^2(L/2)+w(L/2-x)`
`=1/(4piepsilon_0).(Q.q)/h^2(L/2)`
`x=L/2[1+(Qq)/((4piepsilon_0)wh^2)]`
b. There will be no force from the bearing it, w=net electrostatic repulsion from both the charges.
`:. w=1/(4piepsilon_0).(Q(3q))/h^2`
`or h=sqrt((3Qq)/(4piepsilon_0w))`