If the temperature of a wire is doubled then Young's modulus of elasticity ......

Options

A. will also double.
B. will become four times.
C. reamin same.
D. decreases.

Answer

D

Explanation

The change in length of wire occur due to change in temperature.
`L _(t) = L _(0) (1 + alpha Delta T)`
where `Delta T` is the change in temperature, `L _(0)=` original length, `L_(t)` is length at temperature `t, alpha=`coefficient of linear expansion.
`therefore L _(T) - L _(0) = L _(0) prop Delta T`
`therefore Delta L - L _(v) ~~ Delta T" "...(1)`
Now Young.s modulus `Y = ("Stress")/("Strain") = (F//A)/(Delta L //L _(0)) = (FL _(0))/( A Delta L )`
`= (FL _(0))/( AL _(0) prop Delta T) ` [ From eq. (1)]
`therefore Y prop (1)/(Delta T)`
(ALl other terms are constant)
Hence, Y decrease with increasing temperature.