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A Student While Doing An Experiment Finds That The Velocity Of An Object Varies With Time And It Can Be Expressed As Equation: V = Xt2 + Yt +z . If Units Of V And T Are Expressed In Terms Of Si Units, Determine The Units Of Constants X, Y And Z In The Given Equation? |
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Answer» Given, v = Xt2 + Yt +Z Dimensions of velocity v = [M0L1T-1] Applying applying principle of homogeneity in dimensions, TERMS MUST have same dimension. [v] = [Xt2] + [Yt] + [Z] ∴ [v] = [Xt2] ⇒ [X] = [v] /[t2] = [M0L1T-1] / [M0L0T2] = [M0L1T-3] ….(i) SIMILARLY, [v] = [Yt] ⇒ [Y] = [v] / [t] = [M0L1T-1]/ [M0L0T-1] = [M0L1T-2] …(ii) Similarly, [v]= [Z] [Z] = [M0L1T-1] …(III) ⇒ Unit of X = m-s-3 ⇒ Unit of Y = m-s-2 ⇒ Unit of Z = m-s-1 Given, v = Xt2 + Yt +Z Dimensions of velocity v = [M0L1T-1] Applying applying principle of homogeneity in dimensions, terms must have same dimension. [v] = [Xt2] + [Yt] + [Z] ∴ [v] = [Xt2] ⇒ [X] = [v] /[t2] = [M0L1T-1] / [M0L0T2] = [M0L1T-3] ….(i) Similarly, [v] = [Yt] ⇒ [Y] = [v] / [t] = [M0L1T-1]/ [M0L0T-1] = [M0L1T-2] …(ii) Similarly, [v]= [Z] [Z] = [M0L1T-1] …(iii) ⇒ Unit of X = m-s-3 ⇒ Unit of Y = m-s-2 ⇒ Unit of Z = m-s-1 |
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