Question

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

Answer 1

Answer: (A)

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

Answer 2

By substituting the dimension of each quantity we get $T = \lbrack ML^{- 1}T^{- 2}\rbrack^{a}\lbrack L^{- 3}M\rbrack^{b}\lbrack MT^{- 2}\rbrack^{c}$

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