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Question

A thin wire of length 99 cm is fixed at both ends. The wire has some tension and is divided into three segments of lengths l1,l2, and l3 as shown in the figure. If these segments are made to vibrate, with their fundamental frequencies respectively in the ratio 1:2:3, then the lengths l1,l2,l3 respectively are (in cm):


A
27 , 54 , 18
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B
18 , 27 , 54
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C
54 , 27 , 18
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D
27 , 9 , 18
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Solution

The correct option is C 54 , 27 , 18
We know from law of lengths, n1l

l1:l2:l3=1n1:1n2:1n3

From the data given in the question,

l1:l2:l3=1:12:13=6:3:2

Let common factor be 'a'

Then, 6a+3a+2a=99a=9

l1=6a=6×9=54 cm

l2=3a=3×9=27 cm

l3=2a=2×9=18 cm

Thus, option (c) is the correct answer.

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