• # question_answer A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced in the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope? A)  0.06 m                       B)  0.03 mC)  0.12 m                       D)  0.09 m

Since, the rope has a finite mass, the tension in the rope is different at different points on the rope. At the top where the rope is rigidly fixed, the tension = weight of the rope + weight attached to the free end = 6 + 2 = 8 kg wt. Tension at the free end of the rope = 2 kg wt. $\because$$v\propto \sqrt{T},$ if the tension becomes 4 times, the frequency is doubled. Since,$v=\frac{v}{\lambda },\lambda =\frac{1}{v}.$Hence, wavelength is halved.                   Hence, the correction option is [b].