A metal rope of density 6000kgm^-3 has breaking stress 9.8×10⁸ Nm^–2. This rope is used to measure the depth of the sea. Then the depth of the sea that can be measured without breaking is -----

dr = 6000kgm^-3; S = 9.8 x 10⁸ N/m^-2
l = length of rope = Depth of sea.
T_max = Maximum tension induced in the rope
= weight of rope - Buoyant force
= Ald_rg - Ald_wg
= (d_r - d_w)Alg
 At the upper most section of the rope, maximum stress is induced in the rope.

$S_{max}=\frac{T_{max}}{A}=(d_R-d_{\mathrm{w}})lg$
$\therefore l=\frac{S_{max}}{(d_r-d_w)g}=\frac{9.8\times {10}^8}{(6000-1000)\times 9.8}m=20\times {10}^3\mathrm{m}$