Q134 / 150 · MHT CET 2020 (20 Oct Shift 1) · Physics

The ratio of length of two wires of same material is $1: 2$ and the ratio of their radii is $1: \sqrt{2}$. If they are stretched by the same force, the ratio of increase in their lengths is

  • A
    $\sqrt{2}: 2$
  • Correct answer
    B
    $1: 1$
  • C
    $2: \sqrt{2}$
  • D
    $1: 2$

Solution

$Y=\frac{F l}{\pi r^{2} \Delta l}$ or $\Delta l=\frac{F l}{\pi r^{2} Y}$ $\Delta l \propto \frac{l}{r^{2}}, \quad \Delta l^{\prime} \propto \frac{2 l}{(\sqrt{2} r)^{2}}$ or $\Delta l^{\prime} \propto \frac{l}{r^{2}}$ $\therefore \frac{\Delta l}{\Delta l^{\prime}}=1$

Hence, the correct answer is option: 'B'.

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