Question

If the unit of length be doubled then the numerical value of the universal gravitation constant will become:
Gm,m
(with respect to present value) (Use relation F=Gm1m2/r2

(B) Half
(A) Double
(D) 1/8 tmes
(C) 8 times​

Answer 1

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Answer :-

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

Explaination :-

The gravitational force is defined as:

Where, m₁ = mass of the first object

m₂ = mass of the second object

r = distance

G = gravitational constant

The dimension formula of the gravitational constant is

If the unit of length be doubled then,

The unit of new gravitational constant

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

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