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Q.

A student forgot Newton's formula for speed of sound but he remembers that there were speed (v), pressure (p) and density (d) in the formula. He then starts using dimensional analysis to find the actual relation by assuming v∝pxdy. The value of x-y is:

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Detailed Solution

v∝pxdy⇒[v]=pxdy⇒LT−1=ML−1T−2xML−3y By comparing powers of M,L and Tx+y=0,−x−3y=1,−2x=−1⇒ x=12,y=−12⇒ x−y=12−−12=1
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