Answer
1.2m
Work Step by Step
We know that in the given scenario
$\sum T_p=0$
$\implies Tsin\theta\times 2.3=(M+m)g\times \frac{2.3}{2}$
This simplifies to:
$T=\frac{(M+m)g}{2sin\theta}$
We plug in the known values to obtain:
$T=\frac{(66+8.2)\times 9.8}{2sin\theta}$
$T=\frac{363.6}{sin\theta}$
We also know that
$tan\theta=\frac{h}{2.3}$ , hence $sin\theta=\frac{h}{\sqrt{h^2+2.3^2}}$
As given that the maximum tension is 800N
so $T<800N$
$\implies 363.6\sqrt{h^2+(2.3)^2}<800h$
After taking square on both sides, we obtain:
$(363.6)^2(h^2+2.3^2)\frac{363.6\times 2.3}{\sqrt{(800)^2-(363.6)^2}}=1.2m$
Thus, the minimum height should be greater than 1.2m
