Newton’s law of universal gravitation is expressed as F = G

PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

Newton’s law of universal gravitation is expressed as

F = G\,\frac{m_1 m_2}{r^{2}},

where

F

is the gravitational force between two point masses

m_1

and

m_2

separated by a distance

r

, and

G

is the universal gravitational constant. (i) Identify whether

G

is a base quantity or a derived quantity. (ii) Derive the dimensional formula for

G

. (iii) Express

G

in SI base units. (iv) The speed

v

of a satellite in a stable circular orbit of radius

r

around a planet of mass

M

is given by

v = k\sqrt{\dfrac{G M}{r}},

where

k

is a numerical constant. Using dimensional arguments only, show that

k

is dimensionless and that the expression for

v

has the correct dimension of speed.