Velocity of a small ball of mass M and density d₁, when dropped in a container filled with

English

Gujarati

Hindi

9-1.Fluid Mechanics

normal

The velocity of a small ball of mass $M$ and density $d_1,$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $d_2,$ the viscous force acting on the ball will be

A

$Mg\,\left( {1 - \frac{{{d_1}}}{{{d_2}}}} \right)$

B

$Mg\,\left( {1 - \frac{{{d_2}}}{{{d_1}}}} \right)$

C

$Mg\,\,d_1$

D

$Mg\,\,d_2$

Solution

At equilibrium, the viscous force acting upward $=$ Effective force downward

Effective force $=\mathrm{Vd}_{1} \mathrm{g}-\mathrm{Vd}_{2} \mathrm{g}=\mathrm{V}\left(\mathrm{d}_{1}-\mathrm{d}_{2}\right) \mathrm{g}$

$=\frac{M}{d_{1}}\left(d_{1}-d_{2}\right) g=M g\left[1-\frac{d_{2}}{d_{1}}\right]\left[\because V=\frac{M}{d_{1}}\right]$

Standard 11

Physics

Share

Similar Questions

The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac {3H}{4}$ form the upper surface of water, will be

normal

Application of Bernoulli's theorem can be seen in

normal

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, $R$ is equal to

normal

What is the pressure on a swimmer $20 \,m$ below the surface of water is ….. $atm$

normal

Air is streaming past a horizontal aeroplane wing such that its speed is $120\, m/s$ over the upper surface and $90\, m/s$ at the lower surface. If the density of air is $1.3\, kg/m^3$ and the wing is $10\, m$ long and has an average width of $2\, m$ , then the difference of the pressure on the two sides of the wing is …….. $N/m^2$

normal