A uniform rope of length 10 m and mass 3 kg hangs vertically from a rigid support. A block of mass 1 kg is attached to the free end of the rople. A transverse pulse of wavelength 0.05 m is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

Options

A. 0.10 m
B. 0.12 m
C. 0.16 m
D. 0.18 m

Answer

A

Explanation

Since the rope has a mass, the tension along its length is variable. At the top end, its tension is `(3+1)g N` or `4g N`. At the bottom end, its tension is 1g N.
Now, speed of the transverse wave on the string, `c=sqrt((T)/(mu))`
`upsilonlambda=sqrt((T)/(mu))" "(because c=upsilonlambda)`
As frequency `upsilon and mu`, the linear density are constant, so `sqrt(T)/(lambda)`is a constant.