InterviewSolution
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InterviewSolution
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Check the dimensional consistency of the following equations : (i) `upsilon = u +at` (ii) `s = ut +(1)/(2) at^2` (iii) `upsilon^2 - u^2 = 2as` |
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Answer» (i)This equation gives the relation for average velocity , `v_"av"` checking the dimensions on both sides. Average velocity `[V_"av"]=[LT^(-1)]to` L.H.S. Initial velocity `[u]=[LT^(-1)] to` R.H.S. Final velocity `[v]=[LT^(-1)]` Since all the terms have the same dimensions , the equation is dimensionally consistent . But it is not correct physically. The correct expression for average velocity for the given case is `v_"av"="u+v"/2` (ii)`s=ut+1/2at^2` [s]=[L] `to` L.H.S. [ut]=[u][t] `=[LT^(-1)][T]` [ut]=[L] `to` R.H.S. `[1/2at^2]=[LT^(-2)][T^2]=[L] to` R.H.S. Each term of the given equation has the same dimensions, namely that of length . Hence, the equation is dimensionally consistent. It is correct physically too. (iii)`v^2-u^2="2s"/a` Checking the dimensions on both sides . `[v^2]=[LT^(-1)][LT^(-1)]` `=[L^(-2)T^(-2)] to `L.H.S. `[u^2]=[LT^(-1)][LT^(-1)]` `=[L^2T^(-2)]` `["2s"/a]=[L]/[LT^(-1)]=[T] to` R.H.S. Dimensions of the quantities on both sides are not same. So the equation is not correct dimensionally, and hence , physically it cannot be correct. |
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