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BITSAT 2016 Paper

Section: Physics

Question : 6 of 150

Marks: +1, -0

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 Δx on applying force F, how much force is needed to stretch wire 2 by the same amount?

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Solution:

As shown in the figure, the wires will have the sameYoung’s modulus (same material) and the length of the wire of area of cross-section 3A will be A/3 (same volume as wire 1).

For wire 1,

Y=\frac{\frac{F}{A}}{\frac{\Delta x}{l}}

....(1)

For wire 2,

Y=\frac{\frac{F^{I}}{3A}}{\frac{\Delta x}{\frac{l}{3}}}

...(2)

From (i) and (ii)

\frac{F}{A} \times \frac{l}{\Delta x} = \frac{F'}{3A} \times \frac{l}{3\Delta x} \Rightarrow F'=9F

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