Two wires of equal length and equal cross sectional area are suspended as shown in the figure their young modulii are `y_(1)` and `y_(2)` respectively the equaivalent young 's modulus is

Options

A. `y_(1)+y_(2)`
B. `(y_(1)+y_(2))/(2)`
C. `(y_(1)y_(2))/(y_(1)+y_(2))`
D. `sqrt(y_(1)y_(2))`

Answer

B

Explanation

Given two wires have same length and equal cross - sectional area.

i.e., `l_(1) = l_(2) = l ` and `A_(1) =A_(2) = A`
Suppose m is mass of the hanging load .
From figure `2T = mg`
i.e,m `T= (mg)/(2 )`
Hence stress on each wire `= (T )/(A ) = (m g)/(2A)`
`:. Y_(1) = ("strees")/("strain") = (2A )/(Delta l ) = (mgl)/( 2A Delta l)`
and `Y_(2) = ("stress")/(9 "strain" ) = (2A)/(Delta l ) = (mgl )/(2A Delta l )`
If y be the equivalent Young modulus of the combination
then `Y = (mgl )/( A Delta l ) `
From Eqs (i ) (ii) and (ii) we get
`Y= (Y_(1) + Y_(2))/( 2)`