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 at a point `0.5` m distan

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 at a point `0.5` m distan

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 at a point `0.5` m distance
from lower end will be
A. `5" ms"^(-1) and 2.24 "ms"^(-1)`
B. `10" ms"^(-1) and 3.23 "ms"^(-1)`
C. `7.5" ms"^(-1) and 1.2 "ms"^(-1)`
D. None of these

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - a
Mass pre unit length `m=M/L`
Tension at the point T = mass of x meter of rope `xx g`
`=mxxg`
where, x is the distance of point from lober end.
Veloctiy of transverse wave along the string
`v=sqrt(T/m)=sqrt(x(mg)/m)=sqrt(xg)`
Given, `x=0.5` m and `g = 10 " ms"^(_1)`
` v=sqrt(0.5xx10)=sqrt(5)=2.24 " ms"^(_1)`
At upeer end, the velocity is given by
`v= sqrt(rg)= sqrt(2.5xx10)= 5 " ms"^(-1)`