Answer
$67Kg$
Work Step by Step
We can find the mass of the climber as follows:
$mg=Y(\frac{\Delta L}{L})A$
This can be rearranged as:
$m=\frac{Y(\pi r^2)\Delta L}{gL}$
We plug in the known values to obtain:
$m=\frac{(0.37\times 10^{10}Pa)(54.1\times 10^{-6}m^2)(0.046m)}{(9.8m/s^2)(14m)}$
$m=0.0067\times 10^4Kg$
$m=67Kg$
