The temperature of a wire is doubled. The Young's modulus of elasticity

Options

A. (a)will also doubled
B. (b)will bercome four times
C. (c)will remain same
D. (d)will decrease

Answer

D

Explanation

(d) We know that with increase in temperature length of a wire changes as
`L_(t)=L_(0)(1+alphaDeltaT)`
where `DeltaT` is change in the temperature , `L_(0)` is original length, `alpha` is coefficient of linear expansion and `L_(t)` is length at temperature T.
Now we can write, `DeltaL=L_(t)-L_(0)=L_(0)alphaDeltaT`
Young's modulus (Y) `=("Stress")/("Strain")=(FL_(0))/(A xx DeltaL)=(FL_(0))/(AL_(0)alphaDeltaT) prop (1)/(DeltaT)`
As, `Y prop (1)/(DeltaT)`
When temperature increases `DeltaT` increases, hence, Y decrease.