Measurement: Dimensions, Units, and Significant Figures Dimensional consistency

Question

Measurement: Dimensions, Units, and Significant Figures Dimensional consistency Problom 1 (Dimensional consistency). Consider the formulas (1) and (i). Are the formulas dimensionally consistent? Here -distance, U-8pee, a-acceleration, and t = time. + toto (iu)a (s) (i) is dimensionally consistent; (ii) is dimensionally inconsistent (b) () is dimensionally inconsistent; () is dimensionally consistent (e) (0) and (ii) are both dimensionally consistent (d) (i) and (ii) are both dimensionally inconsistent Problem 2 (Dimensional consistency). Determine whother equations (i) and (ii) below are dimensionally consistent. where= distance, u = velocity, t = time, and a acceleration. (a) (i) is dimensionally consistent; (ii) is dimensionally inconsistent (b) (i) is dimensionally inconsistent; (ii) is dimemsionally consistent (c) 6) and (i) are both dimensionally consistent (d) (0) and () are both dimensionally inconsistent Problem 3 (Dimensional consisteney). Determine whether equations (1) and (ii) below are dimeusioially consistent (i) u=1+1 (ii) ra = +2at where = distance, tr = velocity, t = time, and n = Mceleration. (a) (0) is dimensionally cotusistent. (ii) is diusensiotally inconsisteut (b) (0) is dimenssonially iuconsisteut: (u) is diniensionaly cousistent (e) (G) and (i) are lboth diumensionbally consistetnt

Explanation / Answer

1.

(i) t2 = (x+v0t0)/a

s2= (m + (m/s)s)/ (m/s2)

s2 = m.s2/m

s2 = s2 , Dimensionally consistant

(ii)

v = (x0 -at)/t

m/s = (m - (m/s2)s)/s

  Dimensionally inconsistant

option (a) is correct

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