The escape speed of a body from the surface of a planet of mass and radius is given…

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

The escape speed

v_{e}

of a body from the surface of a planet of mass

M

and radius

R

is given by

v_{e}=\sqrt{\dfrac{2GM}{R}}

where

G

is the universal gravitational constant. (i) Derive the dimensional formula of

G

from the above relation. (ii) Express your result in both bracket notation and explicit power form of the base quantities

[M]

[L]

and

[T]

. (iii) Write the corresponding SI unit of

G

obtained from your dimensional formula.