Ncert Exercises & Solutions

A string of mass 2.5 kg is under the tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in:

1. 1 s

2. 0.5 s

3. 2 s

4. data given is insufficient

(2) Hint: The time to reach the other end depends on the velocity of the wave.

Step 1: Find the speed of the wave.

Mass m = 2.5 kg

μ

= mass per unit length

= \frac{m}{t} = \frac{2.5 kg}{20 m} = \frac{1.25}{10} = 0.125 kg / m

speed v

= \sqrt{\frac{T}{μ}} = \sqrt{\frac{200}{0.125}}

[speed of transverse waves in any string]

Step 2: Find the time taken by the wave to reach the other end.

l = v \times t \Rightarrow 20 = \sqrt{\frac{200}{0.125}} \times t

t = 20 \times \sqrt{\frac{125}{2 \times 10^{5}}} = 20 \times \sqrt{\frac{25 \times 5}{2 \times 10^{5}}}

= 20 \times \sqrt{25 \times \frac{1}{0.4 \times 10^{5}}}

= 20 \times 5 \sqrt{\frac{1}{4 \times 10^{4}}} = \frac{20 \times 5}{2 \times 10^{2}}

= \frac{1}{2} = 0.5 \sec

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