A spherical ball of radius 1 times 10^{-4} ,m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: Radius $r = 1 	imes 10^{-4} \,m$, Density of ball $\sigma = 10^4 \,kg \,m^{-3}$, Density of water $\delta = 10^3 \,kg \,m^{-3}$, Viscosity

Vedclass · Accepted Answer

$20.4$ m

Vedclass · Answer

(C) Given: Radius $r = 1 	imes 10^{-4} \,m$, Density of ball $\sigma = 10^4 \,kg \,m^{-3}$, Density of water $\delta = 10^3 \,kg \,m^{-3}$, Viscosity of water $\eta = 9.8 	imes 10^{-4} \,Pa \cdot s$ (standard value).The terminal velocity $v$ of the ball in water is given by Stokes' Law:$v = \frac{2}{9} \frac{g r^2}{\eta} (\sigma - \delta)$Substituting the values:$v = \frac{2}{9} 	imes \frac{9.8 	imes (10^{-4})^2}{9.8 	imes 10^{-4}} 	imes (10^4 - 10^3)$$v = \frac{2}{9} 	imes 10^{-4} 	imes 9000 = 20 \,m/s$Since the velocity does not change upon entering the water, the velocity acquired after falling through height $h$ must be equal to the terminal velocity $v$.Using the equation of motion $v^2 = 2gh$:$h = \frac{v^2}{2g} = \frac{20^2}{2 	imes 9.8} = \frac{400}{19.6} \approx 20.4 \,m$.

$A$ spherical ball of radius $1 \times 10^{-4} \,m$ and density $10^4 \,kg \,m^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If the velocity of the ball does not change after entering the water, then the value of $h$ is:

Similar Questions

On which factors does terminal velocity depend? Explain.

$A$ solid metallic sphere of radius $r$ is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity,then the terminal velocity of the sphere is proportional to which of the following?

$A$ small metal sphere of mass $M$ and density $d_{1}$,when dropped in a jar filled with liquid,moves with terminal velocity after some time. The viscous force acting on the sphere is ($d_{2} =$ density of liquid,$g =$ gravitational acceleration).

Two metal spheres are falling through a liquid of density $3 \times 10^3 \ kg/m^3$ with the same uniform speed. The material densities of sphere $1$ and sphere $2$ are $8 \times 10^3 \ kg/m^3$ and $11 \times 10^3 \ kg/m^3$ respectively. The ratio of their radii is

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio $16: 9$. The ratio of their surface area is

Vedclass Test Series

Exam Paper Generator

Online Exam Module