Planck' constant h , speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M . Then the correct option(s) is (are)

Step-by-step solution

h = M L 2 T - 1 c = L T - 1 G = M - 1 L 3 T - 2 For unit of length Let L ∝ h x c y G z ⇒ From principle of homogeneity L H S = R H S ⇒ M 0 L T 0 = M L 2 T - 1 x L T - 1 y M - 1 L 3 T - 2 z M 0 L T 0 = M x - z L 2 x + y + 3 z T - x - y - 2 z Comparing we get x - z = 0 2 x + y + 3 z = 1 - x - y - 2 z = 0 Solving we get, x = 1 2 , y = - 3 2 , z = 1 2 L = h G c 3 For unit of mass Let M ∝ h x c y G z Solving in similar manner as above We get x = 1 2 , y = 1 2 , z = - 1 2 M = h c G