If E and G respectively denote energy and gravitational constant, then \(\frac{E}{G}\)  has the dimensions 

CONCEPT:

• Energy - Energy is defined as the capacity to do some work and it is equal to E = mc² 
• Here we have, m as the mass and c as the velocity of light.
• Gravitational constant - The Gravitational constant  is denoted by " G " and it comes from,

⇒\(F = \frac {Gm_1 m_2}{r^2}\)

⇒\(G = \frac {F r^2}{m_1 m_2}\)

here, F is the force, m₁, m₂ is the two masses and r is the distance.

CALCULATIONS:

Energy, E = mc2 

• Dimensional formula of energy

[E] = [M¹(LT^-1)²]

⇒[E] = [M¹ L² T^-2]      ------(1)

and \(G = \frac {F r^2}{m_1 m_2}\)

• Dimensional formula of gravitational constant

[G] = [M^-1 L³ T^-2]      ------(2)

Divide equation (1) and (2), we have

\(\frac{{[E]}}{{[G]}} = \frac{{[{M^1}{L^2}{T^{ - 2}}]}}{{[{M^{ - 1}}{L^3}{T^{ - 2}}]}}\)

⇒ \(\left[ {\frac{E}{G}} \right]\) = [M2 L-1 T0]

Hence, correct option is (2)