Question 266: Properties of Matter

Question

The velocity of a small ball of mass $$0.3 \mathrm{~g}$$ and density $$8 \mathrm{~g} / \mathrm{cc}$$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $$1.3 \mathrm{~g} / \mathrm{cc}$$, then the value of viscous force acting on the ball will be $$x 	imes 10^{-4} \mathrm{~N}$$,  The value of $$x$$ is _________. [use $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}ight]$$

Accepted Answer

$F_{\mathrm{V}}+F_B=m g(v=$ constant $)$
$F_V=m g-F_B$
$=ho_{\mathrm{B}} \mathrm{Vg}-ho_{\mathrm{L}} \mathrm{Vg}$
$=\left(ho_{\mathrm{B}}-ho_{\mathrm{L}}ight) \mathrm{Vg}$
$=(8-1.3) 	imes 10^{+3} 	imes \frac{0.3 	imes 10^{-3}}{8 	imes 10^3} 	imes 10$
$=\frac{6.7 	imes 0.3}{8} 	imes 10^{-2} \quad(\mathrm{~g}=10)$
$=\frac{67 	imes 3}{8} 	imes 10^{-4}=25.125 	imes 10^{-4}$

Properties of Matter

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