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Question: The dimensions of universal gravitational constant are –...

The dimensions of universal gravitational constant are –

A

M−2L2T−2M^{- 2}L^{2}T^{- 2}

B

M−1L3T−2M^{- 1}L^{3}T^{- 2}

C

ML−1T−2ML^{- 1}T^{- 2}

D

ML2T−2ML^{2}T^{- 2}

Answer

M−1L3T−2M^{- 1}L^{3}T^{- 2}

Explanation

Solution

F=Gm1m2d2⇒G=Fd2m1m2F = \frac{Gm_{1}m_{2}}{d^{2}} \Rightarrow G = \frac{Fd^{2}}{m_{1}m_{2}}

1ly=9.46×1015meter[G]=[MLT−2][L2][M2]=[M−1L3T−2]1ly = 9.46 \times 10^{15}meter\lbrack G\rbrack = \frac{\lbrack MLT^{- 2}\rbrack\lbrack L^{2}\rbrack}{\lbrack M^{2}\rbrack} = \lbrack M^{- 1}L^{3}T^{- 2}\rbrack