Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Mechanical Properties of Solids

NTA Abhyas 2020 · Physics · Mechanical Properties of Solids

A wire fixed to the ceiling at one end is being pulled slowly by a...

A wire fixed to the ceiling at one end is being pulled slowly by a force FF at the other end.& If the change in length of the wire is l\text{l}, then the work done by the force F\text{F}& is

Options

  1. AF2l\dfrac{F}{2l}
  2. BFl\text{Fl}
  3. C2Fl\text{2Fl}
  4. DFl2\dfrac{Fl}{2}

Correct answer

D. Fl2\dfrac{Fl}{2}

Step-by-step solution

Young's modulus Y=FLAl\text{Y} = \dfrac{FL}{Al} & ............(i)

∴F=YAlL∴\text{F} = \dfrac{YAl}{L}

or dW=Fdl=YAl(dl)L\text{dW} = \text{Fdl} = \dfrac{\text{YAl}\left(\text{dl}\right)}{L}

or & & ∫dW=YAL∫0lldl=YAl22L∫ \text{dW} = \dfrac{YA}{L}\mathop{∫}_{0}^{l}\text{ldl} = \dfrac{\text{YAl}2}{2\text{L}}

or Work done =YAl22L= \dfrac{\text{YAl}2}{2L} ...............(ii)

From (i) and (ii)

Work done = Fl2\dfrac{Fl}{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 2026A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the… JEE Main 2026The two wires A and B of equal cross-section but of different materials are joined… JEE Main 2026A copper wire of length 3 m is stretched by 3 mm by applying an external force. The… JEE Main 2026The Young's modulus of steel wire of radius r and length L is Y . If the radius r and… JEE Main 2026Two wires as shown in the figure below, made of steel and have breaking stress of 12 ×… JEE Main 2026A cube has side length 5 cm and modulus of rigidity 10^5 N/m ^2 . The displacement… JEE Main 2026A 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