Answer
$Y_3\lt Y_1=Y_2\lt Y_4$
Work Step by Step
The expression for the Young modulus is given as
$Y=\frac{F}{A}(\frac{L}{\Delta L})$
For rod 1:
$Y_1=\frac{F}{A}(\frac{L}{\Delta L})$
For rod 2:
$Y_2=\frac{F}{2A}(\frac{2L}{\Delta L})=Y_1$
For rod 3:
$Y_3=\frac{2F}{2A}(\frac{L}{2\Delta L})=\frac{Y_1}{2}$
For rod 4:
$Y_4=\frac{3F}{A}(\frac{\frac{L}{2}}{\Delta L})=\frac{3Y_1}{2}$
