A disc of radius `a` and mass `m` rests between two light rods, which are smoothly hinged together at point `O` with their ends `A` and `B` resting on a smooth table and are maintained in equilibrium by string `AB` as shown in the figure. Choose the correct option(s).

Options

A. The magnitude of normal force acting on the rod at point `A` is `(mg)/(2)`
B. The magnitude of normal force acting on the rod at point `A` is `(mg)/(2cosalpha)`
C. The tension in the string `AB` is `(mg)/(2)[cotalpha+(a)/(c )sec^(2)alpha]`
D. The tension in the string `AB` is `(mg)/(2)[tanalpha+(a)/(c )cosec^(2)alpha]`

Explanation

For unit length of wire,
`F_(e)=lambdaErArr` electric force
`=lambda(2lambda)/(4piepsilon_(0)l)=(lambda^(2))/(2piepsilon_(0)l)`
`lambdarArr` excess charge per unit length of wire
`F_(m)rArr (mu_(0)l^(2))/(2pil)rArr` magnetic force
According to given question
`F_(@)=F_(m)`
`(lambda^(2))/(2piepsilon_(0)l)=(mu_(0)I^(2))/(2pil)`
`rArr ((1)/(lambda))^(2)=(1)/(epsilon_(0)mu_(0))`
`rArr((ln20)/(piepsilon_(0)V)xx(V)/(R ))^(2)=(1)/(mu_(0)epsilon_(0))`
`rArr R=sqrt((mu_(0))/(epsilon_(0)))((ln20)/(pi))=360Omega`