# 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 | 28th Jun, 2021, 09:03: PM

Expert Answer:

### 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 )

^{-2}]

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

^{3}= 1/8Hence , 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 | 28th Jun, 2021, 10:07: PM

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