Question

The velocity of a body is expressed as $V=G^a{M}^b{R}^c$ where $G$ is gravitational constant, $M$ is mass and $R$ is the radius. The values of exponents $a,b$ and $c$ are:

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

Answer 1

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

$V=G^a{M}^b{R}^c$

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

$M^0{L}^1{T}^{-1}=M^{-a+b}{L}^{3a+c}{T}^{-2a}$

$\Rightarrow -2a=-1\Rightarrow a=\frac{1}{2}$

$-a+b=0\Rightarrow b=\frac{1}{2}$

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