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,$\frac{1}{2}$

Answer 1

The correct option is A $-\frac{3}{2},\frac{1}{2}$,1

By substituting the dimension of each quantity we get T = $\left[M{L}^{-1}{T}^{-2}{]}^a\right[L^{-3}M{]}^b[M{T}^{-2}{]}^c=M^{a+b+c}{L}^{-a-3b}{T}^{-2a-2c}$
$\therefore a+b+c=0,-a-3b=0$ and $-2a-2c=1$
Solving we get, $a=\frac{-3}{2},b=\frac{1}{2}$ and $c=1$