Question

A uniform rope of mass $0.1\, kg$ and length $2.5\, m$ hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point $0.5\, m$ distance from lower end will be :

• A. 5 m/s, 2.24 m/s
• B. 10 m/s, 3.23 m/s
• C. 7.5 m/s, 1.2 m/s
• D. 2.25 m/s, 5 m/s

Answer 1

Answer: (A)

$v =\sqrt{\frac{ T }{ m }},\,\,T =0.1 \times 10=1\, N,\, m =\frac{0.1}{2.5}$
Velocity at upper point $v =\sqrt{1 \times 25}$
$v =5\, m / s$
Now velocity at $0.5\, m$ distance from lower point
$v=\sqrt{\frac{T}{m}} \Rightarrow T=\frac{1}{2.5} \times 0.5$
$=\frac{1}{5} N,\, m=\frac{1}{25}$
$v=\sqrt{\frac{1}{5} \times \frac{25}{1}}=\sqrt{5}=2.24\, m / s$