CBSE Class 11-science Answered
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, 21:03: 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 ,
![begin mathsize 14px style F space equals space G space m squared over d squared end style](https://images.topperlearning.com/topper/tinymce/cache/e89b5d867715c265b388e7b83798ff22.png)
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](https://images.topperlearning.com/topper/tinymce/cache/7cc90370941582b016a5560b59abf432.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/7cc90370941582b016a5560b59abf432.png)
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](https://images.topperlearning.com/topper/tinymce/cache/0b0ae4e12f424c41d067c27f2c863cc3.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/0b0ae4e12f424c41d067c27f2c863cc3.png)
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, 22:07: PM
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