Question

Which body depends upon the acceleration due to gravity

Answer 1

Explanation:

The escape velocity ‘v’ of a body depends upon the acceleration due to gravity (g) of the planet and the radius (R) of the planet is expressed as:

v α ga Rb ⇒ v = k ga Rb, where K is a dimensionless proportionality constant. [v] = [g]a [R]b

[M0L1T–1] = [M0L1T–2]a [M0 L1 T0]b

By equating the corresponding powers,

1 = a + b

–1 = –2a ⇒ a = 1/2

b = 1 – a = 1 – 1/2 = 1/2

∴ v = k √gR