Simple Nature - Light and Matter

goes like this:V = 1 3 Ah[1]A = πr 2[2][3][4]V = 1 3 πr 2 hh = πr 23VIs his algebra correct? If not, find the mistake.⊲ Line 4 is supposed to be an equation for the height, so the unitsof the expression on the right-hand side had better equal meters.The pi and the 3 are unitless, so we can ignore them. In terms ofunits, line 4 becomesm = m2m 3 = 1 m.This is false, so there must be a mistake in the algebra. The unitsof lines 1, 2, and 3 check out, so the mistake must be in the stepfrom line 3 to line 4. In fact the result should have beenh = 3Vπr 2 .Now the units check: m = m 3 /m 2 .Discussion QuestionA Isaac Newton wrote, “. . . the natural days are truly unequal, thoughthey are commonly considered as equal, and used for a measure oftime. . . It may be that there is no such thing as an equable motion, wherebytime may be accurately measured. All motions may be accelerated or retarded.. . ” Newton was right. Even the modern definition of the secondin terms of light emitted by cesium atoms is subject to variation. For instance,magnetic fields could cause the cesium atoms to emit light witha slightly different rate of vibration. What makes us think, though, that apendulum clock is more accurate than a sundial, or that a cesium atomis a more accurate timekeeper than a pendulum clock? That is, how canone test experimentally how the accuracies of different time standardscompare?Section 0.1 Introduction and Review 27