Questions in Units and Measurements

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If \[L\] denotes the inductance of an inductor through which a current \[i\] is flowing, the dimensions of \[L{i^2}\] are
Of the following quantities, which one has dimensions different from the remaining three
A spherical body of mass \[m\] and radius \[r\] is allowed to fall in a medium of viscosity \[\eta \]. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity \[(v)\] is called time constant \[(\tau )\]. Dimensionally \[\tau \] can be represented by
The frequency of vibration \[f\] of a mass \[m\] suspended from a spring of spring constant \[K\]is given by a relation of this type \[f = C\,{m^x}{K^y}\]; where \[C\] is a dimensionless quantity. The value of \[x\] and \[y\] are
The quantities \[A\]and \[B\] are related by the relation, \[m = A/B\], where \[m\] is the linear density and \[A\] is the force. The dimensions of \[B\] are of
The velocity of water waves \[v\] may depend upon their wavelength \[\lambda \], the density of water \[\rho \] and the acceleration due to gravity \[g\]. The method of dimensions gives the relation between these quantities as
The dimensions of Farad are
The dimensions of resistivity in terms of \[M,\,L,\,T\] and \[Q\] where \[Q\] stands for the dimensions of charge, is
The equation of a wave is given by
\[Y = A\sin \omega \left( {\frac{x}{v} - k} \right)\]
where \[\omega \] is the angular velocity and \[v\] is the linear velocity. The dimension of \[k\] is
The dimensions of coefficient of thermal conductivity is

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