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in Nature of Physical World and Measurement by (48.5k points)
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The escape velocity v of a body depends on— 

(i) the acceleration due to gravity ‘g’ of the planet, 

(ii) the radius R of the planet. Establish dimensionally the relation for the escape velocity.

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v ∝ gaRb ⇒ v= kgaRb,

K→ dimensionless proportionally constant

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