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Kepler's Law

If E, G, J an...

Question

If E, G, J and m represent energy, universal gravitational constant, angular momentum and mass respectively, then dimensions of $\frac{E J^{2}}{m^{5} G^{2}}$ are those of:

A

Mass

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B

Length

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C

Time

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D

Angle

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Solution

The correct option is D
Angle

$E = M L^{2} T^{2}, J = M L^{2} T^{- 1}, G = M^{- 1} L^{3} T^{- 2}$
Dimension $= \frac{E J^{2}}{m^{5} G^{2}} = \frac{M L^{2} T^{- 2} [M L^{2} T^{- 1}]}{M^{5} [M^{- 1} L^{3} T^{- 2}]^{2}}$
$= M^{\circ} L^{\circ} T^{\circ}$ =Angle

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