Question

The period of a body under $\text{SHM}$ is represented 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. $a=\frac{-3}{2},b=\frac{1}{2},c=1$
• B. $a=\frac{1}{2},b=\frac{1}{2},c=1$
• C. $a=2,b=1,c=1$
• D. $a=1,b=1,c=1$

Answer 1

The correct option is A $a=\frac{-3}{2},b=\frac{1}{2},c=1$

Given, $T=P^a{D}^b{S}^c$
$\left[T\right]=\left[P{]}^a\right[D{]}^b[S{]}^c$
$\left[T\right]=\left[M{L}^{-1}{T}^{-2}{]}^a\right[M{L}^{-3}{]}^b[M{T}^{-2}{]}^c$
$\left[M^0{L}^{0}T\right]=\left[M^{(a+b+c)}{L}^{(-a-3b)}{T}^{(-2a-2c)}\right]$
Equating the powers of dimensions, we have
$a=\frac{-3}{2},b=\frac{1}{2},c=1$