Answer
8400
Work Step by Step
The N pieces of mohair collectively support the person against the weight of the person $mg=75g$. So, the tension in one piece (T) = mg/N.
$T=\frac{mg}{N}=> N=\frac{mg}{T}-(1)$
Let's apply equation 10.17 $F=Y(\frac{\Delta L}{L_{0}})A$ into one piece of mohair.
$T=Y(\frac{\Delta L}{L_{0}})\pi r^{2}-(2)$
(2)=>(1),
$N=\frac{mg}{Y(\frac{\Delta L}{L_{0}})\pi r^{2}}$ ; Let's plug known values into this equation.
$N=\frac{(75\space kg)(9.8\space m/s^{2})}{(2.9\times10^{9})(0.01)\pi (31\times10^{-6}m)^{2}}\approx8400$
