Question

Two bars $A$ and $B$ of circular cross-section and of same volume and made of the same material are subjected to tension. If the diameter of $A$ is half that of $B$ and if the force applied to both the rods is the same and it is in the elastic limit, the ratio of extension of $A$ to that of $B$ will be

• A. 16
• B. 8
• C. 4
• D. 2

Answer 1

Answer: (A)

16

Answer 2

Young modulus, $Y = \frac{FV}{A^2 \Delta l}$
$Y, F$ and $V$ are constants
$\therefore \:\:\:\:\:\: \Delta l \propto \frac{1}{A^2}$
$\therefore \:\:\: \frac{\Delta l_A}{\Delta l_B} = \frac{D^4_B}{D^4_A} = \frac{D^4_B}{\left( \frac{1}{2} D_B \right)^4} = 16$