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 :

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

Tardigrade Admin · Accepted Answer

v =√( T / m ), T =0.1 × 10=1 N, m =(0.1/2.5) Velocity at upper point v =√1 × 25 v =5 m / s Now velocity at 0.5 m distance from lower point v=√(T/m) ⇒ T=(1/2.5) × 0.5 =(1/5) N, m=(1/25) v=√(1/5) × (25/1)=√5=2.24 m / s

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

5 m/s, 2.24 m/s

10 m/s, 3.23 m/s

7.5 m/s, 1.2 m/s

2.25 m/s, 5 m/s

v=mT​​,T=0.1×10=1N,m=2.50.1​ Velocity at upper point v=1×25​ v=5m/s Now velocity at 0.5m distance from lower point v=mT​​⇒T=2.51​×0.5 =51​N,m=251​ v=51​×125​​=5​=2.24m/s

Q. A uniform rope of mass $0.1 k g$ 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 :