A uniform rope of mass $0.1 k g$ and length $2.45 m$ hangs from a ceiling. The speed of transverse waves in the rope at a point $0.5 m$ from the lower end is

2.21 m s^{- 1}

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4.21 m s^{- 1}

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7.21 m s^{- 1}

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3.21 m s^{- 1}

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Solution

The correct option is A $2.21 m s^{- 1}$
$T = \frac{M}{L} (x) g$
$v = \sqrt{\frac{\frac{M}{L} (x) g}{M / L}} = \sqrt{g x} = \sqrt{9.8 \times 0.5} = 2.21 m / s$

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A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The speed of transverse waves in the rope at appoint 0.5 m from the lower end is approximately

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A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The speed of transverse waves in the rope at a point 0.5 m from the lower end is

The correct option is A 2.21 ms−1T=ML(x)gv=  ⎷ML(x)gM/L=√gx=√9.8×0.5=2.21 m/s

A uniform rope of mass $0.1 k g$ and length $2.45 m$ hangs from a ceiling. The speed of transverse waves in the rope at a point $0.5 m$ from the lower end is

The correct option is A $2.21 m s^{- 1}$
$T = \frac{M}{L} (x) g$
$v = \sqrt{\frac{\frac{M}{L} (x) g}{M / L}} = \sqrt{g x} = \sqrt{9.8 \times 0.5} = 2.21 m / s$