Three bars having length l, 2l and 3l and area of cross-section A, 2 A and 3 A are joined rigidly en

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8.Mechanical Properties of Solids

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Three bars having length $l, 2l$ and $3l$ and area of cross-section $A, 2 A$ and $3 A$ are joined rigidly end to end. Compound rod is subjected to a stretching force $F$. The increase in length of rod is (Young's modulus of material is $Y$ and bars are massless)

A

$\frac{13 F l}{2 A Y}$

B

$\frac{F l}{A Y}$

C

$\frac{3 F l}{A Y}$

D

$\frac{9 F l}{A Y}$

Solution

(c)

If extension of $\operatorname{rod}=x$

$x=x_1+x_2+x_3$

$x_1=\frac{F l}{A Y}, \quad x_2=\frac{2 F l}{2 A Y}, \quad x_3=\frac{3 F l}{3 A Y}$

So $x=\frac{3 F l}{A Y}$

Standard 11

Physics

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