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CBSE Class 11-science Answered

<div>A rope of length L and mass m hangs freely from the ceiling.The velocity of transverse &nbsp;as a function of position x along the rope is proportional to</div> <div>&nbsp;</div> <div>(a)<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=93394efb213bbe1789ba5da2b6d2c431.png" alt="x to the power of 0" align="middle" /></div> <div>(b)<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=4cc3bedeef40642610872595959094f9.png" alt="square root of x" align="middle" /></div> <div>(c)<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=a52edb8b09b6f737eab5fa5bbaaff0a7.png" alt="bevelled fraction numerator 1 over denominator square root of x end fraction" align="middle" /></div> <div>(d)X</div>
Asked by Akanksha Mishra | 20 Mar, 2015, 03:35: PM
Expert Answer
The velocity of transverse wave on a rope is given as
 
begin mathsize 14px style straight v equals square root of straight T over straight mu end root end style
Now, when the rope is hanging, the tension in the string depends on the position x along the rope.
 
T = μgx
 
Hence, we have
 
begin mathsize 14px style straight v equals square root of μgx over straight mu end root equals square root of gx end style
Hence, the correct option is (b)
Answered by Romal Bhansali | 20 Mar, 2015, 06:28: PM
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