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Find the dimension of gravitational constant \'G\' |
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Answer» M-1 L3 T-2 The dimensional formula of gravitational constant is given by,M-1\xa0L3\xa0T-2Where,\tM = Mass\tL = Length\tT = TimeDerivationFrom\xa0Newton’s law of gravitation,Force (F) = [GmM] × r-2Gravitational Constant (G) = F × r2\xa0× [Mm]-1 . . . . (1)Since, Force (F) = Mass × Acceleration = M × [LT-2]∴ The\xa0dimensional formula\xa0of force =\xa0M1\xa0L1\xa0T-2\xa0. . . . (2)On substituting equation (2) in equation (1) we get,Gravitational Constant (G) = F × r2\xa0× [Mm]-1Or, G = [M1\xa0L1\xa0T-2]\xa0× [L]2\xa0× [M]-2\xa0= [M-1\xa0L3\xa0T-2].Therefore, the gravitational constant is dimensionally represented as\xa0M-1\xa0L3\xa0T-2. |
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