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Question: E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then th...

E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of El2m5G2\frac{El^{2}}{m^{5}G^{2}} are

A

(a) Angle

A

(b) Length

A

(c) Mass

A

(d) Time

Explanation

Solution

(a)

Sol. [E]\lbrack E\rbrack = energy = [ML2T−2]\lbrack ML^{2}T^{- 2}\rbrack, [m] = mass = [M], [l] = Angular momentum = [ML2T−1]\lbrack ML^{2}T^{- 1}\rbrack

[G] = Gravitational constant = [M−1L3T−2]\lbrack M^{- 1}L^{3}T^{- 2}\rbrack

Now substituting dimensions of above quantities in

El2m5G2\frac{El^{2}}{m^{5}G^{2}}= [ML2T−2]×[ML2T−1]2[M5]×[M−1L3T−2]2\frac{\lbrack ML^{2}T^{- 2}\rbrack \times \lbrack ML^{2}T^{- 1}\rbrack^{2}}{\lbrack M^{5}\rbrack \times \lbrack M^{- 1}L^{3}T^{- 2}\rbrack^{2}}= [M0L0T0]\lbrack M^{0}L^{0}T^{0}\rbrack

i.e., the quantity should be angle.