A) \[{{l}_{A}}=4{{l}_{B}},\] regardless of masses
B) \[{{l}_{B}}=4{{l}_{A}},\] regardless of masses
C) \[{{M}_{A}}=2{{M}_{B}},\,{{l}_{A}}=2{{l}_{B}}\]
D) \[{{M}_{B}}=2{{M}_{A}},\,{{l}_{B}}=2{{l}_{A}}\]
Correct Answer: B
Solution :
The frequency of vibrations of string is |
\[n=\frac{1}{2\pi }\sqrt{\frac{g}{l}}\] |
Given, \[{{n}_{A}}=2{{n}_{B}}\] |
\[\therefore \] \[\frac{1}{2\pi }\sqrt{\frac{g}{{{l}_{A}}}}=2\cdot \frac{1}{2\pi }\sqrt{\frac{g}{{{l}_{B}}}}\] |
or \[\frac{1}{{{l}_{A}}}=\frac{4}{{{l}_{B}}}\] |
or \[{{l}_{B}}=4{{l}_{A}}\] |
It is obvious from Eq. (i), the frequency of vibrations of strings does not depend on their mass. |
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