Acommercial advertisement shows a pearl falling in a bottle of shampoo. if the diameter d of the pearl is quite small and the shampoo sufficiently viscous, the drag d on the pearl is given by stokes's law, d=3πμvd where v is the speed of the pearl and μ is the fluid viscosity. show that the term on the right side of stokes's law has units of force.

Given that

D=3πμVD

We know that

Unit of μ is N.s/m²

Unit of V is m/s

Unit of D is m.

3 and π are scalar .

3πμVD  = (N.s/m²) x  (m/s)  x m= N

So we can say that right side have unit or force.

i don't understand. explain it clearly

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.