A uniform rope of mass M length L hangs vertically from the ceiling, with lower end free. A disturbance on the rope travelling upwards starting from the lower end has a velocity v. At a point P at distance x from the lower end.

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$v = \sqrt{xg}$

$v = \sqrt{2 xg}$

Tension at point P is mg

Tension at point P is $(\frac{M}{L}) xg$

answer is B, D.

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Detailed Solution

Tension at point P

$T_{p} = (\frac{M}{L}) xg = μxg$

Speed of transverse wave
$\begin{array}{l} V = \sqrt{\frac{T}{μ}} = \sqrt{\frac{μxg}{μ}} = \sqrt{xg} \end{array}$

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