One end of a 60 m long rope of mass 1.8 kg is tied to a rigid horizontal support held high above tlie ground. The rope hangs vertically and kept taut by a weight W suspended at its lower end. Aperson jerks the lower end of the rope sideways in a sinusoidal manner and a transverse wave of freqeuncy 2 Hz and amplitude 10 cm passes along the rope such that there are 2 cycles of the wave in the total length of the rope.

Neglecting the weight of the rope as compared to the suspended weight W and with `g = 10 m//s^2`, answer the following questions.
Mass corresponding to the suspended weight W is:

Options

A. 14.2 kg
B. 10.8 kg
C. 6.6 kg
D. 8.4 kg

Answer

B

Explanation

`mu =1.8/60 = 0.03 kg m^(-1)`
`v = 2Hz,A = 0.01 m, lambda= 30`
`v = sqrt(T/m) = sqrt((Mg)/m) = 60, (Mg)/m = 3600`
`Mg = 108, therefore M = 10.8 kg`