A modified gravitational potential is given by V = − r GM + r 2 A . If the constant A is expressed in terms of gravitational constant (G), mass ( M ) and velocity of light (c), then from dimension

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A modified gravitational potential is given by V = − r GM ​ + r 2 A ​ . If the constant A is expressed in terms of gravitational constant (G), mass ( M ) and velocity of light (c), then from dimensional analysis, A is,

TestHub · Accepted Answer

Hint : V = − r GM ​ + r 2 A ​ [ A ] = [ r ] [ GM ] ​ [ r 2 ] = [ GM ] [ r ] now, we know, r GM ​ gives dimension of c 2 [ r ] [ GM ] ​ = [ c 2 ] ⇒ [ r ] = [ c 2 ] [ GM ] ​ ⇒ [ A ] = [ c 2 ] [ GM ] [ GM ] ​ [ A ] = c 2 G 2 M 2 ​

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