Question

If \(E\), \(M\), \(L\) and \(G\) denote energy, mass, angular momentum and constant of gravitation respectively, then the quantity \( \left(\dfrac{EL^2}{G^2M^5}\right) \) has dimensions of

• A. angle
• B. acceleration
• C. velocity
• D. time

Hint:

Any physical quantity with no dimensions usually represents an angle or a pure number.

Answer 1

The Correct Option is A

Step 1: Write dimensions of given quantities.
\[ [E] = ML^2T^{-2}, \quad [L] = ML^2T^{-1}, \quad [G] = M^{-1}L^3T^{-2} \]

Step 2: Substitute dimensions.
\[ \left[\frac{EL^2}{G^2M^5}\right] = \frac{(ML^2T^{-2})(M^2L^4T^{-2})}{(M^{-2}L^6T^{-4})(M^5)} \]

Step 3: Simplify.
All fundamental dimensions cancel out, giving a dimensionless quantity.

Step 4: Conclusion.
A dimensionless quantity corresponds to an angle.