In the equation X = G^ -1/2 ,h^ 1/2 ,c^ 5/2 , where G- universal gravitation constant, h- Planck's constant and c- velocity of light, the dimensions of X are that of

Step-by-step solution

The dimensional formulas for the given physical quantities are: [G] = [M⁻¹ L^3 T⁻²] [h] = [M L^2 T⁻¹] [c] = [L T⁻¹] Given the expression X = G^ -1/2 h^ 1/2 c^ 5/2 , substituting the dimensions: [X] = [M⁻¹ L^3 T⁻²]^ -1/2 [M L^2 T⁻¹]^ 1/2 [L T⁻¹]^ 5/2 [X] = [M^ 1/2 L^ -3/2 T^1] [M^ 1/2 L^1 T^ -1/2 ] [L^ 5/2 T^ -5/2 ] Combining the powers of M , L , and T : [X] = [M^ 1 2 + 1 2 L^ - 3 2 + 1 + 5 2 T^ 1 - 1 2 - 5 2 ] [X] = [M^1 L^2 T⁻²] The dimensions [M L^2 T⁻²] correspond to Energy. Answer: Energy