A `40 cm` long wire having a mass `3.2 g` and area of cross - section ` 1 mm^(2)` is stretched between the support `40 .05 cm` apart. In its fundamental mode , it vibrates with a frequency `1000//64 Hz`. Find the young's modulus of the wire.

Options

A. 1
B. 2
C. 3
D. 4

Answer

A

Explanation

As linear mass density is
`mu = (3.2gm)/(40cm) = (3.2 xx10^(-3))/(40 xx 10^(-2)) = (3.2)/(40) = (32)/(4000)kg//m`
`l = (lambda)/(2)`
`lambda = 2l`

`n_(0) = (v)/(lambda) = (l)/(2l)sqrt((T)/(mu))`
`(1000)/(64) = (1)/(2 xx 40 xx 10^(-2))sqrt((T)/(32//4000))`
`[(1000)/(64) xx2 xx 40 xx 10^(-2)]^(2) (32)/(4000) = T`
`(1000)/(64) xx (32)/(4000) = T`
`T = (10)/(8)N`
`y = (10//8)/((10^(-6))/((0.5 xx 10^(-2))/(40xx10 ^(-2))) ) =(10^(7))/(8) (40)/((.05)) = 10^(9)N//m^(2)`