A) 30 cm and 90 cm
B) 40 cm and 80 cm
C) 60 cm and 90 cm
D) 30 cm and 60 cm
Correct Answer: C
Solution :
Given: Length, of sonometer wire \[(I)=110\,cm\] and ratio of frequencies = 1 : 2 : 3. We know that frequency (v)\[\propto \frac{1}{l}\]or\[l\propto \frac{1}{v}.\] Therefore AC : CD : DB \[=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}=6:3:2\] Therefore, \[AC=6\times \frac{110}{11}=60\,cm\]and CD \[=3\times \frac{110}{11}=30\,cm.\] Thus \[AD=60+30=90\,cm.\]
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