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NEET PHYSICSMedium

If EE and GG respectively denote energy and gravitational constant, then EG\frac{E}{G} has the dimensions of:

A

[ML0T0][ML^0T^0]

B

[M2L−2T−1][M^2L^{-2}T^{-1}]

C

[M2L−1T0][M^2L^{-1}T^0]

D

[ML−1T−1][ML^{-1}T^{-1}]

Step-by-Step Solution

The dimensional formula for energy (EE) is [ML2T−2][ML^2T^{-2}]. The dimensional formula for the universal gravitational constant (GG) is [M−1L3T−2][M^{-1}L^3T^{-2}]. Now, substituting these dimensions into the given expression EG\frac{E}{G}: [EG]=[ML2T−2][M−1L3T−2]\left[\frac{E}{G}\right] = \frac{[ML^2T^{-2}]}{[M^{-1}L^3T^{-2}]} [EG]=[M1−(−1)L2−3T−2−(−2)]\left[\frac{E}{G}\right] = [M^{1 - (-1)} L^{2 - 3} T^{-2 - (-2)}] [EG]=[M2L−1T0]\left[\frac{E}{G}\right] = [M^2 L^{-1} T^0]. Thus, the correct dimensional formula is [M2L−1T0][M^2L^{-1}T^0].

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