Two bars A and B of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of A is half that of B. The ratio of extension of A to B will be:

Question

Two bars A and B of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of A is half that of B. The ratio of extension of A to B will be: (A) 16 (B) 2 (C) 1/4 (D) 4

Tardigrade Admin · Accepted Answer

Δ l=(F L/π r2 Y) but V=π r2 L so L=(V/π r2)=(F V/(π r2)2 Y) propto (1/r4) (Δ lA/Δ lB)=((rB/rA))4=((rB/rB)2)4=16

Q. Two bars $A$ and $B$ of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of $A$ is half that of $B$ . The ratio of extension of $A$ to $B$ will be:

16

2

1/4

4

$Δ l = \frac{F L}{π r ^{2} Y}$
but $V = π r^{2} L$
so $L = \frac{V}{π r ^{2}} = \frac{F V}{( π r ^{2} ) ^{2} Y} \propto \frac{1}{r ^{4}}$
$\frac{Δ l _{A}}{Δ l _{B}} = (\frac{r _{B}}{r _{A}})^{4} = (\frac{r _{B}}{r _{B}} 2)^{4} = 16$

Q. Two bars A and B of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of A is half that of B. The ratio of extension of A to B will be:

16

2

1/4

4

Δl=πr2YFL​ but V=πr2L so L=πr2V​=(πr2)2YFV​∝r41​ ΔlB​ΔlA​​=(rA​rB​​)4=(rB​rB​​2)4=16

Q. Two bars $A$ and $B$ of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of $A$ is half that of $B$ . The ratio of extension of $A$ to $B$ will be:

$Δ l = \frac{F L}{π r ^{2} Y}$
but $V = π r^{2} L$
so $L = \frac{V}{π r ^{2}} = \frac{F V}{( π r ^{2} ) ^{2} Y} \propto \frac{1}{r ^{4}}$
$\frac{Δ l _{A}}{Δ l _{B}} = (\frac{r _{B}}{r _{A}})^{4} = (\frac{r _{B}}{r _{B}} 2)^{4} = 16$