A wire of cross-sectional area A is stretched horizontally between...

A wire of cross-sectional area

A

is stretched horizontally between two clamps loaded at a distance

2l

metres from each other. A weight

w

kg suspended from the midpoint of the wire. The strain produced in the wire, (if the vertical distance through which the midpoint of the wire moves down

x < l

) will be

A wire of cross-sectional area A is stretched horizontally between two clamps loaded at a distance 2l metres from each

Options

A $\dfrac{x2}{l2}$
B $\dfrac{2x^{2}}{l2}$
C $\dfrac{x2}{2l^{2}}$
D $\dfrac{x}{2l}$

Correct answer

C. $\dfrac{x2}{2l^{2}}$

Step-by-step solution

From figure the increase in length

∆ l = \left(PR + RQ\right) - PQ

= 2PR – PQ

= 2{\left(l^{2} + x^{2}\right)}^{1 / 2} - 2l = 2l{\left(1 + \dfrac{x^{2}}{l^{2}}\right)}^{1 / 2} - 2l

= 2l\left[1 + \dfrac{1}{2}\dfrac{x^{2}}{l^{2}}\right] - 2l

( By Binomial theorem)

= x^{2} / l

∴ Strain = ∆ l / 2l = x^{2} / 2l^{2}

Practice Mechanical Properties of Solids on Quantrex Academy →

More from Mechanical Properties of Solids

Figure represents the extension ( Δ l ) of a wire of length 1 meter, suspended from the… JEE Main 2026 A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the… JEE Main 2026 The two wires A and B of equal cross-section but of different materials are joined… JEE Main 2026 A copper wire of length 3 m is stretched by 3 mm by applying an external force. The… JEE Main 2026 The Young's modulus of steel wire of radius r and length L is Y . If the radius r and… JEE Main 2026 Two wires as shown in the figure below, made of steel and have breaking stress of 12 ×… JEE Main 2026 A cube has side length 5 cm and modulus of rigidity 10^5 N/m ^2 . The displacement… JEE Main 2026 A metal string A is suspended from a rigid support and its free end is attached to a… JEE Main 2026 Full Mechanical Properties of Solids list All NTA Abhyas JEE Main PYQs