Question 201: Properties of Matter

Question

If the terminal speed of a sphere of gold (density $$ = 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (density $$ = 1.5\,\,kg/{m^3}$$, find the terminal speed of a sphere of silver (density $$ = 10.5\,\,kg/{m^3}$$) of the same size in the same liquid

Accepted Answer

Let Terminal velocity = v
t
Upward viscous force = downward weight of sphere
$$ \Rightarrow 6\pi \eta r{v_t} = \left( {{4 \over 3}\pi {r^3}} ight)\left( {ho  - \sigma } ight)g$$
$$ \Rightarrow {v_t} = {{2{r^2}\left( {ho  - \sigma } ight)g} \over {9\eta }}$$ ........ (1)
where, $$ho $$ = density of substance of a body
$$\sigma $$ = density of liquid
Now let the terminal velocity of gold = v
g
and silver = v
s
.
From equation (1), we can write
$${{{v_g}} \over {{v_s}}} = {{{ho _g} - \sigma } \over {{ho _s} - \sigma }}$$ $$ = {{19.5 - 1.5} \over {10.5 - 1.5}}$$ = $${{18} \over 9}$$ $$ = {2 \over 1}$$
$$	herefore$$ $${v_s} = {{{v_g}} \over 2}$$ = $${{0.2} \over 2}$$ = 0.1

Answer

$$0.4$$ $$m/s$$

Answer

$$0.133$$ $$m/s$$

Answer

$$0.1$$ $$m/s$$

Answer

$$0.2$$ $$m/s$$

Properties of Matter

If the terminal speed of a sphere of gold (density $ = 19.5\,\,kg/{m^3}) is 0.2 m/s in a viscous liquid (density = 1.5\,\,kg/{m^3}, find the terminal speed of a sphere of silver (density = 10.5\,\,kg/{m^3}$) of the same size in the same liquid

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