A uniform rope of mass 0.1kg and length 2.45m hangs from a ceiling. The speed of a transverse wave in the rope at a point 0.5m distant from the lower end, and the time taken by a transverse wave to travel the full length of the rope respectively are $(g = 9.8 m / s^{2})$

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$\sqrt{9.8} m / s$ , 4 sec

$\sqrt{4.9} m / s$ , 2 sec

$\sqrt{4.9} m / s$ , 1 sec

$\sqrt{9.8} m / s$ , 3 sec

answer is A.

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Detailed Solution

$V = \sqrt{\frac{M g x L}{L M}} = \sqrt{g x} V = \sqrt{g x} = \sqrt{9.8 \times 0.5} = \sqrt{4.9} m s^{- 1}$

$t = 2 \sqrt{\frac{l}{g}} = 2 \sqrt{\frac{2.45}{9.8}} = \frac{2}{2} = 1 \sec$

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