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Two Wires a and B Are Made of Same Material. the Wire a Has a Length L and Diameter Rwhile the Wire B Has a Length 2l and Diameter R/2. - Physics


Two wires A and B are made of same material. The wire A has a length l and diameter rwhile the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is 


  • 1/8

  • 1/4

  • 4

  • 8

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\[\text{ Let the Young's modulus of the wire's material be Y .} \]

\[\text{ Here: }\]

\[\text{ Force = F }\]

\[ A_1 = \pi r^2 \]

\[ L_1 = l\]

\[ A_2 = \pi \left( \frac{r}{2} \right)^2 = \frac{\pi r^2}{4}\]

\[ \text{ L }_2 = 2\text{l }\]

\[\text{ Let the elongation in A be x and that in B be y }. \]

\[\text{ Since the Young's modulus for both the wires is the same: } \]

\[Y = \frac{\frac{F}{A_1}}{\frac{x}{l}} = \frac{\frac{F}{A_2}}{\frac{y}{2l}}\]

\[ \Rightarrow \frac{x}{y} = \frac{A_2}{2 A_1}\]

\[ \Rightarrow \frac{x}{y} = \frac{1}{8}\]

  Is there an error in this question or solution?
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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 14 Some Mechanical Properties of Matter
MCQ | Q 4 | Page 298
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