Question

E, m, L, G represent energy, mass, angular momentum and gravitational constant respectively. The dimensions of \[ \frac{EL^2}{mG^2} \] will be that of 

• A. Angle
• B. Length
• C. Mass
• D. Time

Hint:

Dimensionless quantities, such as angles, are often derived from ratios of similar physical quantities.

Answer 1

The Correct Option is A

Step 1: Define the dimensional formulas 
We use the standard dimensional formulas: - Energy \( E = [ML^2T^{-2}] \) - Mass \( m = [M] \) - Angular momentum \( L = [ML^2T^{-1}] \) - Gravitational constant \( G = [M^{-1}L^3T^{-2}] \) 
Step 2: Compute the dimensions of \( \frac{EL^2}{mG^2} \) 
\[ \frac{EL^2}{mG^2} = \frac{[ML^2T^{-2}] \times [ML^4T^{-2}]}{[M] \times [M^{-2}L^6T^{-4}]} \] \[ = \frac{M^2L^6T^{-4}}{M^{-2}L^6T^{-4}} \] \[ = M^2L^6T^{-4} \times M^2L^{-6}T^{4} \] \[ = M^4 L^0 T^0 \] Since the final expression is dimensionless, it represents an angle, as angles are dimensionless quantities. 
Step 3: Conclusion 
Thus, the correct answer is: \[ \boxed{\text{Angle }} \]