Write principle of Homogeneity of dimension.

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Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

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If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.

$1$ $joule$ of energy is to be converted into new system of units in which length is  measured in $10\, m$, mass in $10\, kg$ and time in $1$ $minute$ then numerical value of  $1\, J$ in the new system is 

If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.