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 ,   begin mathsize 14px style F space equals space G space m squared over d squared end style  
where G is universal gravitational constant
Hence Gravitational constant G is written as  ,  begin mathsize 14px style G space equals space fraction numerator F space cross times space d squared over denominator m squared end fraction end style
Dimensions of force F = [ M L S-2 ]
 
Dimension of distance d = [ L ]
 
Dimension of mass m = [ M ]
 
Dimension of G  begin mathsize 14px style equals space fraction numerator open square brackets M space L space S to the power of negative 2 end exponent close square brackets space open square brackets L squared close square brackets over denominator open square brackets M squared close square brackets end fraction space equals space open square brackets M to the power of negative 1 end exponent space L cubed space S to the power of negative 2 end exponent space close square brackets end style
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 | 28th Jun, 2021, 10:07: PM