If Surface tension ( S ) , Moment of Inertia ( I ) and Planck's constant ( h ) , were to be taken as the fundamental units, the dimensional formula units, the dimensional formula for linear momentum would be:

Question

If Surface tension ( S ) , Moment of Inertia ( I ) and Planck's constant ( h ) , were to be taken as the fundamental units, the dimensional formula units, the dimensional formula for linear momentum would be:, S 1 / 2 I 1 / 2 h 0, S 1 / 2 I 3 / 2 h - 1, S 3 / 2 I 1 / 2 h 0, S 1 / 2 I 1 / 2 h - 1

MARKS App · Accepted Answer

P ∝ S a I b h c [ M L T - 1 ] = M T - 2 a M L 2 b M L 2 T - 1 C M L T - 1 = [ M a + b + c L 2 b + 2 c T - 2 a - c ] From comparing the power on both side a + b + c = 1 2 b + 2 c = 1 - 2 a - c = - 1 From the above three equations we will get a = 1 2 , b = 1 2 & c = 0 P ∝ S 1 2 I 1 2 h 0

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