E,m,p and G denotes energy, mass, angular momentum and gravitational constant. Then which option can be equivalent to (E p2/m5 G2) in dimensions.

Question

E,m,p and G denotes energy, mass, angular momentum and gravitational constant. Then which option can be equivalent to (E p2/m5 G2) in dimensions. (A) Length (B) Mass (C) Angle (D) Time

Tardigrade Admin · Accepted Answer

E=ML2T- 2;m=M;p=ML2T- 1 G=M- 1L3T- 2 ∴ (E p2/m5 G2)=(M L2 T- 2 ⋅ M2 L4 T- 2/M5 ⋅ M- 2 L6 T- 4)= no dimension ∴ it represent angle which has no dimension.

Q. $E, m, p$ and $G$ denotes energy, mass, angular momentum and gravitational constant. Then which option can be equivalent to $\frac{E p ^{2}}{m ^{5} G ^{2}}$ in dimensions.

Length

Mass

Angle

Time

$E = M L^{2} T^{- 2}; m = M; p = M L^{2} T^{- 1}$
$G = M^{- 1} L^{3} T^{- 2}$
$∴ \frac{E p ^{2}}{m ^{5} G ^{2}} = \frac{M L ^{2} T ^{- 2} \cdot M ^{2} L ^{4} T ^{- 2}}{M ^{5} \cdot M ^{- 2} L ^{6} T ^{- 4}} =$ no dimension
$∴$ it represent angle which has no dimension.

Q. E,m,p and G denotes energy, mass, angular momentum and gravitational constant. Then which option can be equivalent to m5G2Ep2​ in dimensions.