1.

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).

Answer»

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

Solution :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`


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