Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L , which of the following statement (s) is/are correct?

Step-by-step solution

M = M a s s = M 0 L 0 T 0 J = A n g u l a r m o m e n t u m = M L 2 T - 1 L = L e n g t h [Now as angular momentum is dimensionless] M L 2 T - 1 = M 0 L 0 T 0 ∴ L 2 = T ∴ P o w e r P = M L T - 2 ⋅ L T - 1 a s P = F ⋅ V = M L 2 T - 3 = L 2 L - 6 ⇒ [ P ] = [ L - 4 ] ⇒ ( A ) is incorrect. Energy/Work W = M L T - 2 ⋅ L (using, W o r k = F o r c e × d i s p l a c e m e n t = L 2 L - 4 = L - 2 ⇒ D is correct. F o r c e F = M L T - 2 = L ⋅ L - 4 = L - 3 ⇒ ( B ) is correct. Linear momentum P = M L T - 1 = L ⋅ L - 2 p = L -