Question

An iron bar of length $ l{\text{ }}cm $ and area of cross section $ {\text{A }}c{m^2} $ is pulled by a force of $ F $ dynes iron ends so as to produce an elongation $ \Delta l{\text{ }}cm $ . Which of the following statements is correct?
(A) Elongation is inversely proportional to length
(B) Elongation is directly proportional to cross section $ {\text{A}} $
(C) Elongation is inversely proportional to $ {\text{A}} $
(D) Elongation is directly proportional to Young’s modulus

Answer 1

Hint : To solve this question, we need to use the formula for the Young’s modulus of a string in terms of its geometrical parameters. Then, putting the values given in the question, we can get the required value of the Young’s modulus of the material wire.

Formula used: The formula which has been used to solve this question is given by
 $ Y = \dfrac{{Fl}}{{A\Delta l}} $ , here $ Y $ is the young’s modulus of a string of length $ l $ and area of cross section $ A $ , $ F $ is the force applied on it due to which its length gets changed by $ \Delta l $ .

Complete step by step answer
We know that the Young’s modulus for a wire can be written as
 $ Y = \dfrac{{Fl}}{{A\Delta l}} $
So we get the elongation as
 $ \Delta l = \dfrac{{Fl}}{{AY}} $ -----------(1)
From equation (1) we can easily observe that the elongation $ \Delta l $ is directly proportional to the length of the iron bar.
So the option A is incorrect.
Also, the elongation is inversely proportional to the area of cross section $ {\text{A}} $ .
So option B is also incorrect.
At the same time option C is correct.
Finally, the elongation is inversely proportional to the Young’s modulus.
So the option D is also incorrect.
Hence, the only correct answer is option C.

Note
We should not worry about the units of the quantities given in the question. They all belong to the CGS system of units. And also if they did not belong to the same system of units, we do not have to worry about converting them. This is because the proportionality between the quantities does not depend on their units.