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Question 26

Match the List I With List II:

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Where (Plank's constant), G(gravitational constant) and c (speed of light in vacuum) as fundamental units.
Choose the  correct answer from the options given below:

Speed of light ($$c$$): $$[c] = [L T^{-1}]$$

Planck's constant ($$h$$): From $$E = h\nu \implies [h] = \frac{[M L^2 T^{-2}]}{[T^{-1}]} = [M L^2 T^{-1}]$$

Gravitational constant ($$G$$): From $$F = \frac{G M^2}{R^2} \implies [G] = \frac{[M L T^{-2}][L^2]}{[M^2]} = [M^{-1} L^3 T^{-2}]$$

$$\left[ \sqrt{\frac{Gh}{c^3}} \right] = [L]$$

$$\left[ \sqrt{\frac{Gh}{c^5}} \right] = [T]$$

$$\left[ \sqrt{\frac{hc}{G}} \right] = [M]$$

[$$\sqrt{\frac{K^2 L^2 c^3}{Gh}}$$] = $$[K]$$

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