Question

a metal sphere of radius 1mm falls vertically in glycerine. find the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1cm/s . Coefficient of viscosity at room temperature is 8.0 poise. plzzxxzz help me out​

Answer 1

Given:
Radius of metallic sphere r = 1 mm = 10−3 m
Speed of the sphere v = 10−2 m/s
Coefficient of viscosity η = 8 poise = 0.8 decapoise
Mass m = 50 mg = 50 × 10−3 kg
Density of glycerin σ = 1260 kg/m3

(a)
Viscous force exerted by glycerine on the sphere F = 6πηrv
⇒ F= 6 × (3.14) × (0.8) × 10−3 × (10−2)
= 1.50 × 10−4 N

(b)
Let V be the volume of the sphere.
Hydrostatic force exerted by glycerin on the sphere F'=Vσg
⇒F'=43πr2σg
=(43)×(3.14)×(10−6)×1260×10=5.275×10−5 N

(c)
Let the terminal velocity of the sphere be v'.
The forces acting on the drops are
(i) The weight mg acting downwards
(ii) The force of buoyance, i.e., 43πr3σg acting upwards
(iii) The force of viscosity, i.e., 6πηrv' acting upwards


6πηrv'+43πr3σg=mg⇒v=mg−43πr2σg6πηr =50×10−3−43×3.14×10−6×1260×106×3.14×0.8×10−3 =500−43×3.14×10−3×1260×106×3.14×0.8 =2.3 cm/s
.
I have some extra answers also.....

Answer 2

⭐Hola User_____________

⭐Here is your answer....!!!

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↪Actually welcome to the concept of the ViSCOSITY

↪The Viscous force is always according to the stokes law that is

↪F = 6 (pi) (n) (r) V

↪here , n (eta) = coeffiect of the ViSCOSITY

↪r = radius and V = Velocity

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