Question

M.K.S. unit of Young’s modulus is
A. $M/m$
B. $M/{m^2}$
C. $M \times m$
D. $M \times {m^2}$

Answer 1

Young’s modulus is given by the division of normal stress by longitudinal strain. It is the property that measures the tensile stiffness of a material. The normal stress depends upon force and area and the longitudinal strain deals with the original length and the length that increases or decreases due to elasticity.

Formula Used:
The formula for Young’s modulus is $Y = \dfrac{{{\sigma _n}}}{{{\varepsilon _l}}}$
where, ${\sigma _n}$ is the normal stress and${\varepsilon _l}$is the longitudinal strain.

Complete step by step answer:
The ratio of the normal stress to the longitudinal strain is called Young's modulus. It is generally denoted as $Y$. And, the formula of Young’s modulus is given by
$Y = \dfrac{{{\sigma _n}}}{{{\varepsilon _l}}}$
where, ${\sigma _n}$ is the normal stress and${\varepsilon _l}$ is the longitudinal strain.

But, ${\sigma _n} = \dfrac{F}{a}$, where $F$is the stretching force and $a$ is the area of the cross section. Also, ${\varepsilon _l} = \dfrac{l}{L}$, where $l$ is the change in length and $L$ is the original length.

\Rightarrow Y= \dfrac{{FL}}{{al}}$$ Therefore, the units of Young’s modulus is: $$\therefore\dfrac{{N.m}}{{{m^3}}} = \dfrac{N}{{{m^2}}}$$ **Hence, option B is the correct answer.** **Note:** The dimensions of Young’s modulus can also be given by modulus of elasticity. The modulus of elasticity is defined as the ratio of stress to strain. Since, strain is a unit less quantity, therefore, the unit of modulus of elasticity is the same as that of stress. Hence, the modulus of elasticity is also expressed as Newton per meter square.