Question

The escape velocity of a body depends on mass of the body, radius of earth and acceleration due to gravity. Derive an expression for escape velocity using dimension analysis

Answer 1

Answer:

Explanation:

v = k gᵃ Rᵇ

where, k= dimensionless constant.

now 

[v] = [ gᵃ Rᵇ ]

[L T ⁻¹] = [(LT ⁻²)ᵃ Lᵇ]

By getting the values of L and T equalized on both sides we will get

a + b = 1

or

-1 = -2a

 a = ½

 b = ½

Therefore   v ∝ (gR)½

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