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Standard XII

Physics

Young's Modulus of Elasticity

Two wires of ...

Question

Two wires of different materials each of length $l$ and cross sectional area ‘ $A$ ’ are joined in series to form a composite wire. If their Young’s modulii are $Y$ and $2 Y$ , the total elongation produced by applying a force $F$ to stretch the composite wire.

3 F A / 2 Y l

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2 F A / 3 Y l

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2 F A / 3 A Y

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3 F l / 2 A Y

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Solution

The correct option is B $3 F l / 2 A Y$
Applying a force F to stretch is applied on both wires simultaneously so we can directly add the elongation of each wire with force F, so,
$Y = \frac{F / A}{△ L_{1} / L}$ for wire with youngs modulus $Y$
$2 Y = \frac{F / A}{△ L_{2} / L}$ for wire with youngs modulus $2 Y$
$△ L_{1} = \frac{F L}{Y A}$
$△ L_{2} = \frac{F L}{2 Y A}$
$△ L_{1} + △ L_{2} = \frac{F L}{Y A} + \frac{F L}{2 Y A} = \frac{3 F L}{2 Y A}$

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Two wires of different materials each of length l and cross sectional area ‘A’ are joined in series to form a composite wire. If their Young’s modulii are Y and 2Y, the total elongation produced by applying a force F to stretch the composite wire.

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