If $E, M, J$ and $G$ respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of $\frac{E J^{2}}{M^{5} G^{2}}$ is:

time

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angle

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mass

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length

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Solution

The correct option is D angle
Dimensions of the given quantity are $\frac{M L^{2} T^{- 2} {[M L^{2} T^{- 1}]}^{2}}{M^{5} {[M^{- 1} L^{3} T^{- 2}]}^{2}} = [M^{0} L^{0} T^{0}]$

Since, the given quantity is dimensionless, among the given options, it can only have dimensions same as angle.

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E, m, J and G denote energy, mass, angular momentum and gravitational constant respectively.

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If E,M,J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of EJ2M5G2 is:

The correct option is D angleDimensions of the given quantity are ML2T−2[ML2T−1]2M5[M−1L3T−2]2=[M0L0T0]Since, the given quantity is dimensionless, among the given options, it can only have dimensions same as angle.

If $E, M, J$ and $G$ respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of $\frac{E J^{2}}{M^{5} G^{2}}$ is:

The correct option is D angle
Dimensions of the given quantity are $\frac{M L^{2} T^{- 2} {[M L^{2} T^{- 1}]}^{2}}{M^{5} {[M^{- 1} L^{3} T^{- 2}]}^{2}} = [M^{0} L^{0} T^{0}]$

Since, the given quantity is dimensionless, among the given options, it can only have dimensions same as angle.