First slide

Dimensions of physical quantities

Question

The period of a body under SHM is respected 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

Moderate

A

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

$- 1, - 2, 3$
C

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

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

Solution

By substituting the dimensions of each quantity, we get
$T = {[M L^{- 1} T^{- 2}]}^{a} {[L^{- 3} M]}^{b} {[M T^{- 2}]}^{c}$
By solving, we get
$a = - \frac{3}{2}, b = \frac{1}{2} a n d c = 1$

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