Question

Breaking stress of an iron rope is 6x10^6 Pa. w It is used to measure depth of sea. The maximum depth that can be measured with the iron rope is (Young's modulus of iron is 5x10^10 Pa, density of iron is 4000 kg/m3, g=10m/s2)
(a) 150 m (b) 175m (c) 200 m (d) 250 m​

Answer 1

Given :

Breaking stress of iron rope = 6 × 10⁶ pa

Young's modulus of iron = 5 × 10¹⁰ pa

Density of iron = 4000 kg/m³

To Find :

The maximum depth that can be measured with the iron rope

Solution :

we know that,

$\sf Breaking \: stress = \dfrac{Breaking \: force}{ Area}$

By substituting the formula,

$\dashrightarrow \sf B.s = \dfrac{B.f}{ A}$

$\dashrightarrow \sf B.s = \dfrac{mg \bigg(1 - \dfrac{p}{d} \bigg)}{ A}$

$\dashrightarrow \sf B.s = \dfrac{ \not Aldg \bigg(1 - \dfrac{p}{d} \bigg)}{ \not A}$

$\dashrightarrow \sf B.s = ldg \bigg(1 - \dfrac{p}{d} \bigg)$

$\dashrightarrow \sf B.s = lg (d - p)$

$\dashrightarrow \sf 6 \times {10}^{6} = l \times 10(4000 - 1000)$

$\dashrightarrow \sf 6 \times {10}^{6} = l \times 10(3000)$

$\dashrightarrow \sf 6 \times {10}^{6} = l \times30000$

$\dashrightarrow \sf l = \dfrac{6 \times {10}^{6} }{3 \times {10}^{4} }$

$\dashrightarrow \sf l = 2 \times {10}^{2}$

$\dashrightarrow \sf l = 200 \: m$

Thus, the maximum depth that can be measured with the iron rope is 200 m

Option (3) 200 m is correct option.

Answer 2

$Breaking \: stress =Lρg$

$6×10 {}^{2} =L×4000×10$

$L=1.5×100 \: \\ L=150m$

The maximum depth that can be measured with the iron rope is 150 m.