Three bars having length l, 2 l and 3 l 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)

Question

Three bars having length l, 2 l and 3 l 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) (13 F I/2 A Y) (B) (F I/A Y) (C) (9 F l/A Y) (D) (3 F l/A Y)

Tardigrade Admin · Accepted Answer

If extension of rod =x x=x1+x2+x3 Where x1, x2, x3 are individual extensions in rod 1, 2, 3 x1=(F l/A Y), x2=(2 F l/2 A Y), x3=(3 F l/3 A Y) So x=(3 F l/A Y)

Q. Three bars having length $l, 2 l$ and $3 l$ 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)

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

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

$\frac{9 Fl}{A Y}$

$\frac{3 Fl}{A Y}$

If extension of rod $= x$
$x = x_{1} + x_{2} + x_{3}$
Where $x_{1}, x_{2}, x_{3}$ are individual extensions in rod $1, 2, 3$
$x_{1} = \frac{Fl}{A Y}, x_{2} = \frac{2 Fl}{2 A Y}, x_{3} = \frac{3 Fl}{3 A Y}$
So $x = \frac{3 Fl}{A Y}$

Q. Three bars having length l,2l and 3l and area of cross-section A,2A and 3A 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)

2AY13FI​

AYFI​

AY9Fl​

AY3Fl​