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Dimensions of physical quantities

Question

A stone is lying at rest in a river. The minimum mass of stone, m=kρvxg3 is needed to remain at rest. Here, k = constant having no unit, g = acceleration due to gravity, v = river flow velocity , ρ = density of water. The value of x is_________________

Moderate
Solution

The unit of LHS is kg. The unit of RHS should be kg.

 Here, kρvxg3=kgm3msxms23=(kg)(m)3+x3(s)+6x 6+x=0 x=6



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