Gravitation Question 217

Question: Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area $ [A] $ and wire 2 has cross-sectional area$ [3A] $ . If the length of wire 1 increases by Ax on applying a force $ [F] $ , how much force is needed to stretch wire 2 by the same amount?

Options:

A) $ [F] $

B)$ [4F] $

C) $ [6F] $

D) $ [9F] $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ [A_{1}l_{1}=A_{2}l_{2}] $

    $ [\Rightarrow l_{2}=\frac{A_{1}l_{1}}{A_{2}}=\frac{A\times l_{1}}{3A}] $

    $ [\Rightarrow \frac{l_{1}}{l_{2}}=3] $ $ [\Delta x_{1}=\frac{F_{1}}{A\gamma }\times l_{1}] $

    $ [\Rightarrow x_{2}=\frac{F_{2}}{3A\gamma }\times l_{1}] $ Here $ [\Delta x_{1}=\Delta x_{2}] $

    $ [\frac{F_{2}}{3A\gamma }l_{2}=\frac{F_{1}}{A\gamma }l_{1}\Rightarrow F_{2}=3F_{1}\times \frac{l_{1}}{l_{2}}=3F_{1}\times 3=9F] $



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