Question

In the shown arrangement, the end A of string is fixed to the rigid support and end B is kept free. A transverse pulse is produced at P at t = 0, which moves towards right. If the shape of the string changes periodically, then its time period is…... [Tension in the string = 80N. Mass per unit length of string is 0.2 kg/m]

• A. 0.4 s
• B. 0.1 s
• C. 0.2 s
• D. 0.6 s

Answer 1

The correct option is C 0.2 s

Speed of transverse jerk on the string = v, say = $\sqrt{\frac{T}{\mu }}$
Shape of string at t = 0
Shape of string at t = $2\frac{\left(PB\right)}{v}$
Shape of string at t = $2\left(\frac{PA}{v}\right)$
Shape of string at t = $2\left(\frac{PB}{v}\right)$
Shape of string at t = $2\left(\frac{PA}{v}\right)$
Hence the required the period, T $=\frac{4AB}{v}$
Putting the values, we get 0.2 sec.