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

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

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.