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A wave pulse starts propagating in positive $x -$ direction along a non-uniform wire of length $10 m$ with mass per unit length given $m = m_{0} + α x$ and under a tension of $100 N$ . The time taken by the pulse to travel from the lighter end $(x = 0)$ to the heavier end $x = 10 m$ is
$(g i v e n m_{0} = 10^{- 2} k g m^{- 1} a n d α = 9 \times 10^{- 3} k g m^{- 2})$ $(i n \sec)$

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answer is B.

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Detailed Solution

$V = \frac{d x}{d t} = \sqrt{\frac{T}{m}} = \sqrt{\frac{T}{m_{0} + α x}}$

$∴ (\sqrt{m_{0} + α x}) d x = \sqrt{T} d t$

$\int_{0}^{10} (\sqrt{m_{0} + α x}) d x = \sqrt{T} \int_{0}^{t} d t$

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