Question

A metallic beam having Young's modulus $Y$ is supported at the two ends. It is loaded at the centre. The depression of the centre is proportional to

• A. $Y$
• B. $1/Y$
• C. $Y^2$
• D. $1/Y^2$

Answer 1

The correct option is B $1/Y$

Depression in the beam is given by $\delta =\frac{W{L}^3}{4Yb{d}^3}$

where $W$ is the weight,$L$ is length,$b$ is breadth, $Y$ is young's modulus and $d$ is the depth and $\delta$ is the depression in the beam.

Here, it is clear that,

Depression in the beam is inversely proportional to Young's modulus

$\delta \propto \frac{1}{Y}$