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Dimensional Analysis

If the unit o...

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

d o u b l e

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B

h a l f

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C

8 t i m e s

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D

1 / 8 t i m e s

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Solution

The correct option is C $1 / 8 t i m e s$
$∵ n_{1} u_{1} = n_{2} u_{2}$
$∴ \frac{n_{2}}{n_{1}} = \frac{u_{1}}{u_{2}} = \frac{M_{1}^{- 1} L_{1}^{3} T_{1}^{- 2}}{M_{2}^{- 1} L_{2}^{3} T_{2}^{- 2}} = \frac{M^{- 1} L^{3} T^{- 2}}{M^{- 1} (2 L)^{3} T^{- 2}} = \frac{1}{8}$

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