Question

A sphere of radius R moving with a velocity V under stream line conditions in a viscous experiences a retarding force F given by F=krv where k is a constant. the s.i unit of k in terms of the base units.
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Answer 1

Answer:

[ F ]= [ K ] [ r ] [ v ]

kg• m•s−2 = [ K ] (m) (m•s−1)

[ K ] =kg• m−1 • s-1

Answer 2

The SI. unit of k is $kgm^{-1} s^{-1}$.

• The fluids and the apparatus will be utilised in a range of physical quantities throughout this book. Quantitative descriptions of these quantities are necessary, necessitating sets of measurements and units For instance, a fluid's density is a significant factor that typically affects how the fluid behaves.
• A set of units must be chosen for each of the dimensions to be used in order to give the density a numerical value. In this book, the SI (Système International) system will be used to specify all units. This is true for a good reason: the SI is the only coherent practical system of units. This means that when solving problems, conversion factors are never needed.

Here, F is given as F = kRV.

Then, k = $\frac{F}{RV}$

Or, F = $\frac{[MLT^{-2}] }{[L][LT^{-1}] }$ = $[ML^{-1}T^{-1}]$

Hence, the SI. unit of k is $kgm^{-1} s^{-1}$.

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