Mechanical Properties Of Solids Ques 1
1. Two wires are made of the same material and have the same volume. The first wire has crosssectional area $A$ and the second wire has cross- sectional area $3A$. If the length of the first wire is increased by $\Delta \ell$ on applying a force $\mathrm{F}$, how much force is needed to stretch the second wire by the same amount?
[2018]
(a) $9 \mathrm{F}$
(b) $6 \mathrm{F}$
(c) $\mathrm{F}$
(d) $4 \mathrm{F}$
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Answer:
Correct Answer: 1.(a)
Solution: (a) Wire 1:
$ \Delta \ell=\left(\frac{F}{A Y}\right) 3 \ell $ $\quad$ ……..(i)
Wire 2:
$ \Delta \ell=\left(\frac{F^{\prime}}{3 A Y}\right) \ell $ $\quad$ ……..(ii)
From equation (i) & (ii),
$ \Delta \ell=\left(\frac{F}{A Y}\right) 3 \ell=\left(\frac{F^{\prime}}{3 A Y}\right) \ell \text { or, } F=9 F $
BETA
