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Q.

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

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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 is A.

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Detailed Solution

$\begin{array}{rcl} [L T^{- 1}] α {[M^{- 1} L^{3} T^{- 2}]}^{a} {[M]}^{b} {[L]}^{c} \\ [L T^{- 1}] α [M^{- a + b} L^{3 a + c} T^{- 2 a}] \\ - a + b & = & 0 - - - (1) \\ 3 a + c & = & 1 - - - (2) \\ - 2 a & = & - 1 - - - (3) \\ s o l v i n g (1 (2) (3) w e g e t a & = & b = \frac{1}{2} & c = \frac{- 1}{2} \end{array}$

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