A metal sphere of radius $1 m m$ and mass $50 m g$ falls vertically in glycerine. Find the hydrostatic force exerted by the glycerine on the sphere.

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Solution

Given data,
Radius of metallic sphere $r = 1 m m = 10^{- 3} m$
Speed of the sphere $v = 10^{- 2} m / s$
Mass $m = 50 m g = 50 \times 10^{- 3} k g$
Density of glycerin $σ = 1260 k g / m^{3}$
Hydrostatic force exerted by glycerin on the sphere $F^{'} = ?$
We know that
Let $v$ be the volume of the sphere.
Hydrostatic force exerted by glycerin on the spere $F^{'} = V σ g$
$\Rightarrow F^{'} = \frac{4}{3} π r^{3} σ g$
$= (\frac{4}{3}) \times (3.14) \times (10^{- 6}) \times 1260 \times 10$
$= 5.275 \times 10^{- 5} N$

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A metal sphere of radius 1mm and mass 50mg falls vertically in glycerine. Find the hydrostatic force exerted by the glycerine on the sphere.

A metal sphere of radius $1 m m$ and mass $50 m g$ falls vertically in glycerine. Find the hydrostatic force exerted by the glycerine on the sphere.