Question

The velocity of a body is expressed as v =G*Mºre where G is gravitational constant, M is mass, R is radi
values of components a, b&c are​

Answer 1

Correct Question:-

The velocity of a body is expressed as $\sf{v=G^a\,M^b\,R^c}$ where G is gravitational constant, M is mass and R is radius. Find values of $\sf{a,\ b}$ and $\sf{c.}$

Solution:-

We're given,

$\longrightarrow\sf{v=G^a\,M^b\,R^c}$

Taking dimensions of each term,

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

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

Equating powers of corresponding quantities, we get,

$\longrightarrow\sf{-a+b=0}$

$\longrightarrow\sf{3a+c=1}$

$\longrightarrow\sf{-2a=-1}$

On solving these three equations, we get,

$\longrightarrow\underline{\underline{\sf{a=\dfrac{1}{2}}}}$

$\longrightarrow\underline{\underline{\sf{b=\dfrac{1}{2}}}}$

$\longrightarrow\underline{\underline{\sf{c=-\dfrac{1}{2}}}}$