A uniform wire of length 20 m and weighing 5 kg hangs vertically. If $g = 10 m / s^{2}$ , then the speed of transverse waves in the middle of the wire is

10 m / s

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10 \sqrt{2} m / s

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4 m / s

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0

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Solution

The correct option is A $10 m / s$
Here, $μ = \frac{5}{20} k g / m = \frac{1}{4} k g / m$

Tension in the middle of wire,
$T =$ weight of half the wire $= \frac{5}{2} \times g = \frac{5}{2} \times 10 N = 25 N$

As, $v = \sqrt{\frac{T}{μ}} \Rightarrow v = \sqrt{\frac{25}{1 / 4}} = 10 m / s$

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A uniform wire of length 20 m and weighing 5 kg hangs vertically. If g=10m/s2, then the speed of transverse waves in the middle of the wire is

The correct option is A 10 m/sHere, μ=520 kg/m=14 kg/mTension in the middle of wire, T= weight of half the wire =52×g=52×10N=25NAs, v=√Tμ⇒v=√251/4=10 m/s

A uniform wire of length 20 m and weighing 5 kg hangs vertically. If $g = 10 m / s^{2}$ , then the speed of transverse waves in the middle of the wire is

The correct option is A $10 m / s$
Here, $μ = \frac{5}{20} k g / m = \frac{1}{4} k g / m$

Tension in the middle of wire,
$T =$ weight of half the wire $= \frac{5}{2} \times g = \frac{5}{2} \times 10 N = 25 N$

As, $v = \sqrt{\frac{T}{μ}} \Rightarrow v = \sqrt{\frac{25}{1 / 4}} = 10 m / s$