Question

If the unit of length be doubled then the numerical value of the universal gravitation constant G will
become (with respect to present value)
(A) double
(B) hall
(C) 8 times
(D) 1/8times​

Answer 1

Explanation:

Bhai your answer is option D.

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Answer 2

Answer:

The numerical value of universal gravitational constant will be 1/8  times of  G'

The gravitational force is defined as:

$F = \frac{GmM}{r^{2} }$

$G = \frac{Fr^{2} }{Mm}$

Where, m = mass of the first object

M = mass of the second object

r = distance

G = gravitational constant

The dimension formula of the gravitational constant is

$G = [ M^{-1} L^{3} T^{-2} ]$

If the unit of length be doubled then,

The unit of new gravitational constant is,

$G' = [ M^{-1} (2L)^{3} T^{-2} ]$

$G' = [ M^{-1} 8L^{3} T^{-2} ]$

$G' = 8 * [ M^{-1} L^{3} T^{-2} ]$

$G' = 8G$

The unit of gravitational constant G' becomes 8 times of G.

$G = \frac{G'}{8}$

Hence, The numerical value of universal gravitational constant will be 1/8  times of G'

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