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If E, M, L and G denote energy, mass, an...

If E, M, L and G denote energy, mass, angular momentum and gravitational constant repectively then the quantity `(E^(2)L^(2)//M^(5)G^(2))` has the dimensions of :-

A

angle

B

length

C

mass

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
The dimensions of `E=["ML"^(2)"T"^(-2)]`
Dimensions of M= [M]
Dimensions of L = `["ML"^(2)"T"^(-1)]`
Dimensions of G = `["M"^(-1)"L"^(3)"T"^(-2)]`
`therefore` Dimensions of `[("E"^(2)"L"^(2))/("M"^(5)"G"^(2))]=(["ML"^(2)"T"^(-2)]^(2)["ML"^(2)"T"^(-1)]^(2))/(["M"]^(5)["M"^(-1)"L"^(3)"T"^(-2)]^(2))`
`" "=["ML"^(2)"T"^(-2)]`
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