Q. 30

# A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerin. Find (a) the viscous force exerted by the glycerin on the sphere when the speed of the sphere is 1 cm s’, (b) the hydrostatic force exerted by the glycerin on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerin = 1260 kg m^{-3} and its co-efficient of viscosity at room temperature = 8.0 poise.

Answer :

(a) 1.5 × 10^{-4} N

(b) 5.2 × 10^{-5} N

(c) 2.9 cm s^{-1}

Given, radius of sphere,

Mass of the sphere,

Coefficient of viscosity,

Velocity,

(a)Therefore, viscous force is given by,

(b)The hydrostatic force is equal to the buoyant force of the glycerin which will have the same volume as that of the sphere immersed.

Hence, Force,

(c) Let the terminal velocity be v.

The viscous force,

The upwards force is due to the buoyant force in glycerin.

and the weight downwards,

Hence, as per situation, there should be no acceleration downwards.

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