If C (velocity of light), h (Planck's constant) and G (Universal gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is

Question

If C (velocity of light), h (Planck's constant) and G (Universal gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is, h - 1 2 G 1 2 C o, h 1 2 C 1 2 G - 1 2, h - 1 2 C 1 2 G - 1 2, h - 1 2 C - 1 2 G - 1 2

MARKS App · Accepted Answer

Let, M = C a h b G c M L 0 T 0 = L T - 1 a M L 2 T - 1 b M - 1 L 3 T - 2 c ......(i) Where, h = E n e r g y F r e q y e n c y = M L 2 T - 2 T - 1 = M L 2 T - 1 C = M e t r e S e c o n d = L T - 1 G = F o r c e × d i s t a n c e 2 m a s s 2 = M L T - 2 L 2 M 2 = M - 1 L 3 T - 2 Comparing the coefficients M, L, T, of both sides we get b - c = 1 ......(ii) a + 2 b + 3 c = 0 ......(iii) - a + b + 2 c = 0 .....(iv) Solve the equations (ii), (iii) and (iv), we get a = 1 2 , b = 1 2 , c = - 1 2 So, M = h 1 2 C 1 2 G - 1 2

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