Period of a body under SHM i.e. presented by T = {P^a}{D^b}{S^c} ; where P is pressure, D is density

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1.Units, Dimensions and Measurement

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The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are

A

$ - \frac{3}{2},\,\frac{1}{2},\,1$

B

$ - 1,\, - 2,\,3$

C

$\frac{1}{2},\, - \frac{3}{2},\, - \frac{1}{2}$

D

$1,\,2,\,\frac{1}{3}$

(KVPY-2020)

Solution

(a) By substituting the dimension of each quantity we get

$T = {[M{L^{ – 1}}{T^{ – 2}}]^a}{[{L^{ – 3}}M]^b}{[M{T^{ – 2}}]^c}$

By solving we get $a = -3/2, b = 1/2$and $c = 1$

Standard 11

Physics

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