Question 285: Properties of Matter

Question

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $$3696	imes10^{-x}$$ N. The value of $$x$$ is ________.
(Given, g = 9.8 m/s$$^2$$ and $$\pi=\frac{22}{7}$$)

Accepted Answer

At state of terminal speed, net force on the ball is zero
$	herefore \quad F_{v}=w-F_{B}$
$=\left(\frac{4}{3} \pi R^{3} ho_{b} gight)-\left(\frac{4}{3} \pi R^{3} ho_{l} gight)$
$=\frac{4}{3} \pi R^{3}\left(ho_{b}-ho_{l}ight) g$
$=\frac{4}{3} 	imes \frac{22}{7} 	imes\left(10^{-3}ight)^{3}\left[9 	imes 10^{3}ight] 	imes 9.8$
$=3696 	imes 10^{-7}$
$	herefore x=7$

Properties of Matter

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $3696\times10^{-x} N. The value of x is ________. (Given, g = 9.8 m/s^2 and \pi=\frac{22}{7}$)

Integer / Numeric Answer Type