Question 196: Properties of Matter

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 $$\Delta x$$ on applying force $$F,$$ how much force is needed to stretch wire $$2$$ by the same amount?

Accepted Answer

As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of cross-section $$3A$$ will be $$\ell /3$$ (same volume as wire $$1$$).
For wire $$1,$$
$$y = {{F/A} \over {\Delta x/\ell }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$$
For wire $$2.$$
$$Y = {{F'/3A} \over {\Delta x/\left( {\ell /3} ight)}}........(ii)$$
From $$(i)$$ and $$(ii),$$ $${F \over A} 	imes {\ell  \over {\Delta x}} = {{F'} \over {3A}} 	imes {\ell  \over {3\Delta x}} \Rightarrow F' = 9F$$

Answer

$$4F$$

Answer

$$6F$$

Answer

$$9F$$

Answer

$$F$$

Properties of Matter

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

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