Answer

Verified

349.2k+ views

**Hint:**Stress and strain have a direct proportional relationship up to an elastic limit. The association between stress and strain is explained by Hooke's rule. Hooke's law states that the pressure in a solid is proportional to the applied stress, which must be within the solid's elastic limit.

**Complete step by step answer:**

The elastic modulus is the proportionality constant in this relationship. The general relationship between stress and strain is linear in the linear limit of low stress values.Hence, by Hooke's law we can state the formula as:

Elastic modulus $ = \dfrac{{stress}}{{strain}}$

Stress is characterised as the force applied to an object that causes it to change shape, while strain is defined as the change in shape of an object caused by stress.

Hence, stress can be calculated as:

$stress = \dfrac{F}{A}$ where $F$ is force and $A$ is area.

On the other hand strain can be calculated using the following formula:

$strain = \dfrac{{{l_1} - l}}{l}$

Substituting the above values to the main equation we get,

Elastic modulus $(\gamma ) = \dfrac{F}{A} \times \dfrac{l}{{{l_1} - l}}$

When $4N$ tension is applied,

$\gamma = \dfrac{4}{A} \times \dfrac{l}{{{l_1} - l}} - (i)$

When $5\,N$ tension is applied,

$\gamma = \dfrac{5}{A} \times \dfrac{l}{{{l_2} - l}} - (ii)$

Dividing $(i)$ and $(ii)$ equation, we get,

$ \Rightarrow \dfrac{{{\gamma } = \dfrac{4}{{{A}}} \times \dfrac{{{l}}}{{{l_1} - l}}}}{{{\gamma } = \dfrac{5}{{{A}}} \times \dfrac{{{l}}}{{{l_2} - l}}}} \\$

$\Rightarrow \dfrac{{{l_1} - l}}{{{l_2} - l}} = \dfrac{4}{5} \\

\Rightarrow 5({l_1} - l) = 4({l_2} - l) \\

\Rightarrow 5{l_1} - 5l = 4{l_2} - 4l \\

\Rightarrow 5{l_1} - 4{l_2} = l \\ $

Now, for $9\,N$ tension , we can write,

$\gamma = \dfrac{9}{A} \times \dfrac{l}{{l' - l}} - (iii)$

We will now compare $(i)$ and $(iii)$

$\Rightarrow \dfrac{{{\gamma } = \dfrac{4}{{{A}}} \times \dfrac{{{l}}}{{{l_1} - l}}}}{{{\gamma } = \dfrac{9}{{{A}}} \times \dfrac{{{l}}}{{l' - l}}}} \\$

$\Rightarrow \dfrac{{{l_1} - l}}{{l' - l}} = \dfrac{4}{9} \\

\Rightarrow 9({l_1} - l) = 4(l' - l) \\

\Rightarrow 9{l_1} - 9l = 4l' - 4l \\

\Rightarrow 9{l_1} - 5l = 4l' \\ $

Now , substituting $l$ value we get,

$9{l_1} - 5(5{l_1} - 4{l_2}) = 4l' \\

\Rightarrow 9{l_1} - 25{l_1} + 20{l_2} = 4l' \\

\Rightarrow - 16{l_1} + 20{l_2} = 4l' \\

\therefore l' = 5{l_2} - 4{l_1} \\ $

**Hence, the correct option is C.**

**Note:**A strain is a dimensionless quantity with no variable, while stress is a measurable quantity with a unit. The terms "stress" and "strain" come from the Latin words "strictus" and "stringere," respectively, which mean "to draw close" and "to tie firmly." Stress may exist without strain, but strain does not exist in the absence of stress.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE