Solveeit Logo
Login

Question

Question: Young’s modulus of steel is \(1.9 \times {10^{11}}N{m^{ - 2}}\). Express it in CGS units. (Given \...

Young’s modulus of steel is 1.9×1011Nm−21.9 \times {10^{11}}N{m^{ - 2}}. Express it in CGS units.
(Given 1N=105dyne1N = {10^5}dyne, 1m2=104cm21{m^2} = {10^4}c{m^2})
A. 1.9×1010 B. 1.9×1011 C. 1.9×1012 D. 1.9×1013  {\text{A}}{\text{. 1}}{\text{.9}} \times {\text{1}}{{\text{0}}^{10}} \\\ {\text{B}}{\text{. 1}}{\text{.9}} \times {\text{1}}{{\text{0}}^{11}} \\\ {\text{C}}{\text{. 1}}{\text{.9}} \times {\text{1}}{{\text{0}}^{12}} \\\ {\text{D}}{\text{. 1}}{\text{.9}} \times {\text{1}}{{\text{0}}^{13}} \\\

Explanation

Solution

We need to convert the units of Young’s modulus into units of the CGS system. We are given the relation between the SI units and the CGS units. By directly inserting them into the given value, we can get the required value of Young’s modulus in CGS units.

Complete answer:
We are given the value of Young’s modulus of steel in SI units. It is given as
Y=1.9×1011Nm−2Y = 1.9 \times {10^{11}}N{m^{ - 2}}
We are required to express it in CGS units. In order to do that, we need to convert the given units of Young’s modulus into a CGS system.
For the SI unit of force, which is newton, the relation with the CGS unit dyne is given as
1N=105dyne1N = {10^5}dyne
For the SI unit of length, which is metre, the relation with the CGS unit centimetre is given as
1m2=104cm21{m^2} = {10^4}c{m^2}
Now we can convert the given value to CGS units by directly inserting these conversions into the given value. It can be done in the following way.
Y=1.9×1011Nm−2=1.9×1011×105dyne104cm2=1.9×1012dyne/cm2Y = 1.9 \times {10^{11}}N{m^{ - 2}} = 1.9 \times {10^{11}} \times \dfrac{{{{10}^5}dyne}}{{{{10}^4}c{m^2}}} = 1.9 \times {10^{12}}dyne/c{m^2}
This is the required value in the CGS units.

Hence, the correct answer is option C.

Note:
1. It should be noted that the Young’s modulus of steel is defined as the ratio of the stress applied on the steel to the strain produced in steel. The large value of the Young’s modulus for steel means that the strain produced in steel is very less for a large amount of stress applied on it.
2. While solving problems, we need to take care that all the units are in the same system of units. The SI system of units is the most commonly used system of units.