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If E , M , J , and G , respectively , de...

If `E , M , J , and G` , respectively , denote energy , mass , angular momentum , and gravitational constant , then `EJ^(2) //M^(5) G^(2)` has the dimensions of

A

mass

B

length

C

time

D

angle

Text Solution

Verified by Experts

The correct Answer is:
D
`[E]=[ML^(2)T^(-2)],[m]=[M]`
`[l]=[ML^(2)T^(-1)],[G]=[M^(-1)L^(3)T^(-2)]`
`therefore[(El^(2))/(m^(5)G^(2))]=([ML^(2)T^(-2)][M^(2)L^(4)T^(-2)])/([M^(5)][M^(-2)L^(6)T^(-4)])=[M^(0)L^(0)T^(0)]`
As angle has no diemsions, therefore `(El^(2))/(m^(5)G^(2))` has the same dimensions as that of angle.
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