Question

the ratio of the terminal velocity of drop a to b if B have A​

Answer 1

see the given attachment

hope it helps you ☺️

Answer 2

Answer:

Thus, the ratio of their terminal velocity =1:4

Explanation:

Let the radius of the smaller ball =r

the radius of the bigger ball=2r

Density of the ball's material=ρ

b

Density of liquid=ρ

Terminal velocity of the balls is v1 and v2 for the smaller and bigger respectively.

Volume of the smaller ball V=

3

4

πr

3

The mass of the ball will be =ρ

b

V

Volume of the bigger ball =

3

4

π(2r)

3

=8V

The mass of the ball will be=8ρ

b

V

Upthrust on the smaller ball=ρV

g

Viscous drag force on smaller ball =6πηrv

1

Weight of the smaller ball =ρ

b

V

g

Now, since the balls are moving with terminal velocity, the total upward force will balance its weight

$$\rho V_g+6\pi \eta rv_1=\rho _bV_g ----1.

Upthrust on the bigger ball =8ρV

g

Viscous drag force on bigger ball =6πη2rv

2

Weight of the bigger ball =8ρ

b

V

g

Similarly,

8ρV

g

+6πη2rv

2

=8ρ

b

V

g

----2.

Dividing eqn. 1 by eqn. 2

8ρVg+12πηrv2

ρVg+6πηrv1

=

8

1

=>8ρV

g

+12πηrv

2

=8ρV

g

+48πηrv

1

=>12πηrv

2

=48πηrv

1

=>v

2

=4v

1

=>

v

2

v

1

=

4

1