If E and G respectively denote energy and gravitational constant, then E/G has dimensions of: - Physics MCQ NEET 2021 2026 | ExamTest.live | ExamTest.live

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If E and G respectively denote energy and gravitational constant, then E / G has dimensions of:

A $[M] [L^{0}] [T^{0}]$
B $[M^{2}] [L^{- 2}] [T^{- 1}]$
C $[M^{2}] [L^{- 1}] [T^{0}]$
D $[M] [L^{- 1}] [T^{- 1}]$

Solution & Step-by-step Explanation

Dimension of Energy [E] = [M L^{2} T^{- 2}] Dimension of Gravitational Constant [G] :From F = G \frac{m _{1} m _{2}}{r ^{2}} \Rightarrow G = \frac{F r ^{2}}{m ^{2}} $ [G] = \frac{[ M L T ^{- 2} ] [ L ^{2} ]}{[ M ^{2} ]} = [M^{- 1} L^{3} T^{- 2}] D im e n s i o n o f E/G : \frac{[ M L ^{2} T ^{- 2} ]}{[ M ^{- 1} L ^{3} T ^{- 2} ]} = [M^{1 - (- 1)} L^{2 - 3} T^{- 2 - (- 2)}] = [M^{2} L^{- 1} T^{0}] $

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If E and G respectively denote energy and gravitational constant, then E / G has dimensions of:

A

[M] [L^{0}] [T^{0}]

B

[M^{2}] [L^{- 2}] [T^{- 1}]

C

[M^{2}] [L^{- 1}] [T^{0}]

D

[M] [L^{- 1}] [T^{- 1}]

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