A wire of cross section A is stretched horizontally between two clamps located 2/ m apart. A weight W kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance x

Question

A wire of cross section A is stretched horizontally between two clamps located 2/ m apart. A weight W kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance x < < l the strain produced is (A) (2x2/l2) (B) (x2/l2) (C) (x2/2l2) (D) none o f these

Tardigrade Admin · Accepted Answer

Here change in length is Δ l = [AC + BC ] - 2l = 2 (I2 + x2)1/2 , - 2 l = 2l ( 1 + (x2/l2) )1/2 = 2 l ( 1 + (1/2) (x2/l2) ) - 2l = (x2/l) ∴ strain = (Δ l/2 l) = (x2/2 l2)

Q. A wire of cross section A is stretched horizontally between two clamps located 2/ m apart. A weight W kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance $x << l$ the strain produced is

$\frac{2 x ^{2}}{l ^{2}}$

$\frac{x ^{2}}{l ^{2}}$

$\frac{x ^{2}}{2 l ^{2}}$

none o f these

Here change in length is
$Δ l = [A C + BC] - 2 l$
= $2 (I^{2} + x^{2})^{1/2}, - 2 l = 2 l (1 + \frac{x ^{2}}{l ^{2}})^{1/2}$
= $2 l (1 + \frac{1}{2} \frac{x ^{2}}{l ^{2}}) - 2 l = \frac{x ^{2}}{l}$
$∴$ strain = $\frac{Δ l}{2 l} = \frac{x ^{2}}{2 l ^{2}}$

Q. A wire of cross section A is stretched horizontally between two clamps located 2/ m apart. A weight W kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance x<<l the strain produced is

l22x2​

l2x2​

2l2x2​