Question

The period of a body under S.H.M. is represented by : $T=P^a{D}^b{S}^c$ where $P$ is pressure, $D$ is density and $S$ is surface tension, then values 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)

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

Let $T=P^a{D}^b{S}^c$
So, $\left[T\right]=\left[M^0{L}^0{T}^1\right]$

$=\left[M{L}^{-1}{T}^{-2}{]}^a\right[M{L}^{-3}{]}^b[M{T}^{-2}{]}^c$

$=\left[M^{a+b+c}{L}^{-a-3b}{T}^{-2a-2c}\right]$

Applying principle of homogeneity,

$a+b+c=0;-a-3b=0;-2a-2c=1$
On solving, we get $a=-3/2.b=1/2,c=1$