Question

A wire of cross section $A$ is stretched horizontally between two clamps located $2lm$ apart. A weight $Wkg$ is suspended from the mid-point of the wire.If the Young's modulus of the material is $Y$, the value of extension $x$ is

• A. ${\left(\frac{Wl}{YA}\right)}^{1/3}$
• B. ${\left(\frac{YA}{WI}\right)}^{1/3}$
• C. $\frac{1}{l}{\left(\frac{Wl}{YA}\right)}^{2/3}$
• D. $l{\left(\frac{W}{YA}\right)}^{2/3}$

Answer 1

The correct option is D $l{\left(\frac{W}{YA}\right)}^{2/3}$

Let $M$, $L$ and $T$ represent the dimensions of mass, length and time respectively. Then:

${\left[\right(\frac{Wl}{YA})}^{\frac{1}{3}}]=\frac{\left[M^{\frac{1}{3}}{L}^{\frac{2}{3}}{T}^{-\frac{2}{3}}\right]}{\left[M^{\frac{1}{3}}{L}^{\frac{2}{3}}{T}^{-\frac{2}{3}}\right]}=[M^0{L}^0{T}^0]$

Since extension has dimensions of length, the only option which fits the requirement is the last one where an additional length term is multiplied.