Question

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

• A. $1,3,1/3$
• B. $\frac{-3}{2},\frac{1}{2},1$
• C. $-1,-2,3$
• D. $\frac{-1}{2},\frac{-3}{2},\frac{-1}{2}$

Answer 1

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

$T\propto P^a{D}^b{S}^c$

$P=M^1{L}^{-1}{T}^{-2}$
$S=M^1{L}^0{T}^{-2}$
$M^0{L}^0{T}^1=\left(M^1{L}^{-1}{T}^{-2}{)}^a\right(M^1{L}^{-3}{)}^b(M^1{T}^{-2}{)}^c$
$0=a+b+c$
$0=-a-3b$
$1=-2a-2c$

$\Rightarrow a=-\frac{3}{2},b=\frac{1}{2},c=1$