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if the unit of length and mass be doubled then the numerical value of w. r. t present value of universal gravitational constant will become
Asked by suhani.pare | 28 Jun, 2021, 09:03: PM
Let us consider gravitational force of attraction F  between two objects of equal mass m that are sepearted by a distance d

Then we have ,
where G is universal gravitational constant
Hence Gravitational constant G is written as  ,
Dimensions of force F = [ M L S-2 ]

Dimension of distance d = [ L ]

Dimension of mass m = [ M ]

Dimension of G
if unit of mass is doubled, then present quantity of mass becomes (1/2) of modified mass .

Since gravitational constant G is inversely prportional to mass ,  G will be increased by a factor 2

if unit of length is doubled, then present length becomes (1/2) of modified length .

Since gravitational constant G is directly prportional to cube of distance ,  G will be decreased by a factor (1/2)3 = 1/8

Hence , modified universal gravitational constant G' = (2/8) G = (1/4)G

Modified universal gravitational constant G' = 0.25 × 6.674 × 10-11 = 1.668 × 10-11 N' (m' )2 (kg')-2

( Where N' , m' and kg' are modified Newton , modified metre and modified kg in new units system )

Answered by Thiyagarajan K | 28 Jun, 2021, 10:07: PM

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