Two identical unifrom rods tied together with the help of a string are balanced as shown in the figure, then.

Choose the correct option(s).

Options

A. If the system is in equilibrium, and the coefficient of frication of friction is `0.8`, then the tension in the string is `(4mg)/(5)`.
B. If the system is in equilibrium, and the coefficient of frication of friction is `0.8`, then the tension in the string is `(2mg)/(5)`.
C. If the system is in equilibrium, and the coefficient of frication of friction is `0.9`, then the tension in the string is `(2mg)/(3)`.
D. If the system is in equilibrium, and the coefficient of frication of friction is `0.9`, then the tension in the string is `(9mg)/(10)`.

Answer

B, C

Explanation

the `FBD` of any one rod is
`T = muN` …….(i)
`mg = N` ……..(ii)

Taking torque about point `'P'`
`mg"(L)/(2)cos37^(@) = TL sin 37^(@)`
`T = (mg)/(2)(4)/(3) = (2mg)/(3)`
`(2mg)/(3) = mumg rArr mu = 2/3`