Question

If $E,\, M,\, J$ and $G$ respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of $\frac{E J^{2}}{M^{5} G^{2}}$

• A. time
• B. angle
• C. mass
• D. length

Answer 1

Answer: (B)

Given quantity is $\frac{E J^{2}}{M^{5} G^{2}}$ ...(i)
where dimensions of the various given quantities are
Dimensions of $E=\left[ ML ^{2} T ^{-2}\right]$
Dimensions of $J=\left[ ML ^{2} T ^{-1}\right]$
Dimension of $M=[ M ]$
Dimension of $G=\left[ M ^{-1} L ^{3} T ^{-2}\right]$
Now, on putting these dimensions in Eq. (i), we have
$=\frac{\left[ ML ^{2} T ^{-2}\right]\left[ ML ^{2} T ^{-1}\right]^{2}}{\left[ M ^{5}\right]\left[ M ^{-1} L ^{3} T ^{-2}\right]^{2}}$
$=\frac{\left[ M ^{3} L ^{6} T ^{-2}\right]}{\left[ M ^{3} L ^{6} T ^{-2}\right]}=$
dimensionless Since, angle is a dimensionless quantity