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I started off with taking kg m/s^2.. Then I wrote all the old units i terms of the new units.. Now the old units are each half of the new units.. So where there was kg, you write KG/2.. Now there are two 1/2s in the numerator, and two in the denominator. Because it is (S/2)^2=S^2/4) So all these 1/2s cancel, leaving N as it is, and the new units in the same form as the old ones..
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