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Byju's Answer

Standard XII

Physics

Young's Modulus of Elasticity

Two wires are...

Question

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

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Solution

The correct option is C 9F
$Y = \frac{F l}{A △ l}$
so, $F = \frac{Y A^{2} △ l}{A l} = \frac{Y A^{2} △ l}{V}$
where, $A l = V =$ Volume of wire
hence $F \propto A^{2}$
$\frac{F^{'}}{F} = \frac{(3 A)^{2}}{A^{2}} = 9$
or F'=9F

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

The correct option is C 9FY=FlA△ l so,F=YA2△ lAl=YA2 △ lV where,Al=V= Volume of wire hence F ∝ A2 F′F=(3A)2A2=9 or F'=9F

The correct option is C 9F
$Y = \frac{F l}{A △ l}$
so, $F = \frac{Y A^{2} △ l}{A l} = \frac{Y A^{2} △ l}{V}$
where, $A l = V =$ Volume of wire
hence $F \propto A^{2}$
$\frac{F^{'}}{F} = \frac{(3 A)^{2}}{A^{2}} = 9$
or F'=9F