InterviewSolution
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InterviewSolution
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The velocity (V) of a particle (in cm/s) is given in terms of time (t) in sec by the equation `V=at+(b)/(c+t)`. The dimensions of a, b and c areA. `{:(a,b,c),(L^(2),T,L^(1)T^(-2)):}`B. `{:(a,b,c),(L^(1)T^(2),L^(1)T,L^(1)):}`C. `{:(a,b,c),(L^(1)T^(-2),L^(1),T^(1)):}`D. `{:(a,b,c),(L^(1),L^(1)T,T^(2)):}` |
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Answer» Correct Answer - c L.H.S. is `V=[L^(1)M^(0)T^(-1)]` Every term has the dimensions of velocity. `therefore at=V therefore a=(V)/(t)` `therefore [a]=(M^(0)L^(1)T^(-1))/(T^(1))=[L^(1)T^(-2)]and(b)/(c+t)=V` But as we can add only the terms with the same dimensions `therefore` C has the dimensions of t. Thus, `C=t therefore b=V" (time)"therefore [b]=[L^(1)T^(-1)xxT^(1)]=L^(1)` Thus, `[a]=L^(1)T^(-2),[b]=L^(1),[c]=T^(1)` |
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