Consider two solid spheres P and Q each of de | vedclass

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

Question

(D) The terminal velocity $v$ of a sphere falling through a viscous liquid is given by the formula: $v = \frac{2gr^2(\rho - \sigma)}{9\eta}$,where $g$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) The terminal velocity $v$ of a sphere falling through a viscous liquid is given by the formula: $v = \frac{2gr^2(ho - \sigma)}{9\eta}$,where $g$ is the acceleration due to gravity,$r$ is the radius of the sphere,$ho$ is the density of the sphere,$\sigma$ is the density of the liquid,and $\eta$ is the coefficient of viscosity.The ratio of terminal velocities is: $\frac{v_P}{v_Q} = \frac{r_P^2(ho_P - \sigma_1) \eta_2}{r_Q^2(ho_Q - \sigma_2) \eta_1}$.Given values:$ho_P = ho_Q = 8 \ g \ cm^{-3}$$r_P = 0.5 \ cm$,$r_Q = 0.25 \ cm$$\sigma_1 = 0.8 \ g \ cm^{-3}$,$\sigma_2 = 1.6 \ g \ cm^{-3}$$\eta_1 = 3 \ 	ext{poiseuille}$,$\eta_2 = 2 \ 	ext{poiseuille}$Substituting these values into the ratio formula:$\frac{v_P}{v_Q} = \frac{(0.5)^2 	imes (8 - 0.8) 	imes 2}{(0.25)^2 	imes (8 - 1.6) 	imes 3}$$\frac{v_P}{v_Q} = \frac{0.25 	imes 7.2 	imes 2}{0.0625 	imes 6.4 	imes 3}$$\frac{v_P}{v_Q} = \frac{3.6}{1.2} = 3$.Thus,the ratio of the terminal velocities is $3$.

Similar Questions

Give the practical uses of viscosity.

$A$ 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).

The average mass of rain drops is $3.0 \times 10^{-5} \, kg$ and their average terminal velocity is $9 \, m/s$. Calculate the energy transferred by rain to each square metre of the surface at a place which receives $100 \, cm$ of rain in a year.

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6 \ cm \ s^{-1}$. If they coalesce to form one big drop,what will be the terminal speed of the bigger drop (in $cm \ s^{-1}$)? (Neglect the buoyancy of the air)

$A$ steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown in the graph below. The terminal velocity of the ball is closest to .......... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module