A) \[5m/s,2.24m/s\]
B) \[10m/s,3.23m/s\]
C) 7.5m/s
D) none of these
Correct Answer: A
Solution :
Mass per unit length \[m=\frac{M}{L}\] Tension at the point T= mass of x meter of rope \[\times \] g \[=mx\,g\] where x is the distance of point from lower end Velocity of transverse wave along the string \[\upsilon =\sqrt{\frac{T}{m}}=\sqrt{x\frac{mg}{m}}=\sqrt{xg}\] Here: \[x=0.5m\,\,g=10m/{{s}^{2}}\] \[\upsilon =\sqrt{0.5\times 10}=\sqrt{5}=2.24m/s\] At upper end, the velocity is given by \[\upsilon =\sqrt{rg}=\sqrt{2.5\times 10}=5m/s\]
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