escape velocity of a body depends upon acceleration due to gravity and radius of planet established dimensionally relation between them
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v = k ga Rb
k is a dimensionless constant.
[v] = [ ga Rb ]
[L T −1] = [(LT −2)a Lb]
Equating the powers of L and T on both sides of the equation, we get
a + b = 1
-1 = -2a
Solving, we get a = ½ and b = ½
Therefore v ∝ (gR)½
v = k ga Rb
k is a dimensionless constant.
[v] = [ ga Rb ]
[L T −1] = [(LT −2)a Lb]
Equating the powers of L and T on both sides of the equation, we get
a + b = 1
-1 = -2a
Solving, we get a = ½ and b = ½
Therefore v ∝ (gR)½
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