A) \[\text{5 m}/\text{s},\text{ 2}.\text{24 m}/\text{s}\]
B) \[\text{1}0\text{ m}/\text{s},\text{ 3}.\text{23 m}/\text{s}\]
C) \[\text{7}.\text{5 m}/\text{s},\text{ 1}.\text{2 m}/\text{s}\]
D) None of the above
Correct Answer: A
Solution :
Velocity of transverse wave along the string is \[{{v}_{T}}=\sqrt{\frac{T}{m}}\] where m is mass per unit length, T the tension. Also \[T=mg\], \[m=\frac{m}{x}\] \[\therefore \] \[{{v}_{T}}=\sqrt{\frac{m\,gx}{m}}=\sqrt{gx}\] Given, \[g=10\,m/{{s}^{2}}\], \[x=0.5\,m\] \[\therefore \] \[{{v}_{T}}=\sqrt{10\times 0.5}\] \[=\sqrt{5}=2.24\,m/s\] At upper end, the velocity is given by \[v=\sqrt{rg}\] \[=\sqrt{2.5\times 10}=5\,m/s\]
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