If E , L , M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL 2 M -5 G -2 are :-

Question

If E , L , M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL 2 M -5 G -2 are :- (A) [ M 0 L 1 T 0] (B) [ M -1 L -1 T 2] (C) [ M 1 L 1 T -2] (D) [ M 0 L 0 T 0]

Tardigrade Admin · Accepted Answer

E = ML 2 T -2 L = ML 2 T 1 m = M G = M -1 L +3 T -2 P =( EL 2/ M 5 G 2) [ P ]=(( ML 2 T -2)( M 2 L 4 T -2)/ M 5( M -2 L 6 T -4)) = M 0 L 0 T 0

Q. If $E, L, M$ and $G$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of $P$ in the formula $P = E L^{2} M^{- 5} G^{- 2}$ are :-

$[M^{0} L^{1} T^{0}]$

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

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

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

$E = M L^{2} T^{- 2}$
$L = M L^{2} T^{1}$
$m = M$
$G = M^{- 1} L^{+ 3} T^{- 2}$
$P = \frac{E L ^{2}}{M ^{5} G ^{2}}$
$[P] = \frac{( M L ^{2} T ^{- 2} ) ( M ^{2} L ^{4} T ^{- 2} )}{M ^{5} ( M ^{- 2} L ^{6} T ^{- 4} )}$
$= M^{0} L^{0} T^{0}$

Q. If E,L,M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P=EL2M−5G−2 are :-

[M0L1T0]

[M−1L−1T2]

[M1L1T−2]

[M0L0T0]