Question

Breaking stress of an iron rope is $6\times {{10}^{6}}Pa$. The rope is used to measure the depth of the sea. The maximum depth can be measured with the iron rope is (Young's modulus of iron is $5\times {{10}^{10}}Pa$ , the density of iron is $4000kg/{{m}^{3}}$ , (g=$10m/{{s}^{2}}$))
A.150m
B. 175m
C. 200m
D. 250m

Answer 1

Hint: The breaking stress is the maximum force per unit area which can be handled by a particular rope. It is also known as the tensile stress of the material. The word tensile means that the material is under certain tension.
Formula used:
Breaking stress = $L\rho g$

Complete answer:
According to the question,
Breaking the stress of iron rope is \[6\times {{10}^{6}}Pa\]
Young’s modulus of iron is $5\times {{10}^{10}}Pa$
The density of iron is $4000\,kg\,{{m}^{-3}}$

The stress applied to the material is equivalent to the force experienced by it per unit area of the material. The maximum value of the stress which can be handled by the body without causing any damage to it is known as the breaking stress.

The breaking stress of a material is mathematically given as,
Stress = $L\rho g$
Where,
For the above question
$L$ is the maximum length which can be measured by the iron rope
$\rho $ is the density of the rope
$g$ is the acceleration due to gravity

By taking account of the information given in the question. The breaking stress can be given as,
$6\times {{10}^{6}}=L(4000)(10)$
By rearranging, the maximum length which can be measured with the help of the iron rope will be,
\[\begin{align}
  & L=\dfrac{6\times {{10}^{6}}}{40000} \\
 & \Rightarrow 150m \\
\end{align}\]
Thus, the maximum depth that can be measured using the mentioned iron rope is 150m.

So, the correct answer is “Option A”.

Note:
Young's modulus of a material is only valid in a range in which the stress is proportional to the strain of the material. It was named after the physicist Thomas Young. Young's modulus is the measurement of the ability of the material to withstand the change in the length when it undergoes lengthwise alterations. If we continuously apply a force after the breaking stress the rope will not be able to handle that and it will break into two parts.