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Q. $ \text{M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{3}}}{{\text{I}}^{\text{-2}}} $ is the dimension of:

JIPMERJIPMER 1996

Solution:

We know that $ M{{L}^{2}}{{T}^{-3}} $ is the dimension of power, hence the given quantity is $ =\frac{\text{power}}{{{\text{(current)}}^{\text{2}}}} $ We also know that $ {{i}^{2}}R=power $ So, $ R=\frac{\text{power}}{{{\text{(current)}}^{\text{2}}}} $ Therefore, $ M{{L}^{2}}{{T}^{-3}}{{I}^{-2}} $ is the dimension of resistance.