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(D) The unit of force is $N$ (Newton),which is $kg\,m\,s^{-2}$.Given unit is $N\,m^{-1}\,s^{-2}$.Substituting the base units of force: $(kg\,m\,s^{-2}

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None of these

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(D) The unit of force is $N$ (Newton),which is $kg\,m\,s^{-2}$.Given unit is $N\,m^{-1}\,s^{-2}$.Substituting the base units of force: $(kg\,m\,s^{-2}) 	imes m^{-1} 	imes s^{-2} = kg\,s^{-4}$.Alternatively,let us check the dimensions: $[N] = [MLT^{-2}]$,$[m^{-1}] = [L^{-1}]$,$[s^{-2}] = [T^{-2}]$.Multiplying these: $[MLT^{-2}] 	imes [L^{-1}] 	imes [T^{-2}] = [MT^{-4}]$.This unit does not correspond to any standard fundamental physical quantity like pressure $(N\,m^{-2})$,surface tension $(N\,m^{-1})$,or force constant $(N\,m^{-1})$.Therefore,the correct option is $D$.

Identify the physical quantity that has the unit $N\,m^{-1}\,s^{-2}$.

Similar Questions

Which of the following pairs of quantities do not have the same dimensions?

The pair$(s)$ of physical quantities that have the same dimensions,is (are)

Which physical quantities have the same dimension?

Fill in the blanks by suitable conversion of units:
$(a)$ $1\; kg\; m^{2}\; s^{-2} = \ldots\; g\; cm^{2}\; s^{-2}$
$(b)$ $1\; m = \ldots\; ly$
$(c)$ $3.0\; m\; s^{-2} = \ldots\; km\; h^{-2}$
$(d)$ $G = 6.67 \times 10^{-11}\; N\; m^{2}\; kg^{-2} = \ldots\; cm^{3}\; s^{-2}\; g^{-1}$

Identify the pair of physical quantities which have different dimensions.

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