A) 1 kg
B) 2 kg
C) 4 kg
D) 16 kg
Correct Answer: D
Solution :
[d] Load supported by sonometer wire = 4 kg Tension in sonometer wire = 4 g If \[\mu =\] mass per unit length then frequency' \[\upsilon =\frac{1}{2l}\sqrt{\frac{T}{\mu }}\] \[\Rightarrow \]\[416=\frac{1}{2l}\sqrt{\frac{4g}{\mu }}\] When length is doubled, i.e.,\[l'=2l\] Let new load =L As, \[\upsilon '=\upsilon \] \[\therefore \]\[\frac{1}{2l'}\sqrt{\frac{Lg}{\mu }}=\frac{1}{2l}\sqrt{\frac{4g}{\mu }}\] \[\Rightarrow \]\[\frac{1}{4l'}\sqrt{\frac{Lg}{\mu }}=\frac{1}{2l}\sqrt{\frac{4g}{\mu }}\] \[\Rightarrow \]\[\sqrt{L}=2\times 2\]\[\Rightarrow \]\[L=16\,kg\]
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