Question

A spherical ball of radius 1*10-4 m and density 104kgm-3 falls freely under gravity through a distance h before entering a tank of water. If after entering the water,the velocity of ball does not change, find h . Coefficient of viscosity of water is 9.8*10-6 pa sec.

Answer 1

Answer:

If the ball's velocity didn't change after entering into water. that means ball achieved terminal velocity as it touched the water surface.

And the terminal velocity V

c

of the body of radius r, density

ρ falling through a medium of density ρ

o

is given by

V

c

=

9η

2r

2

(ρ−ρ

o

)g

where η is the coefficient of viscosity of medium.

V

c

=

9×9.8×10

−6

2×(10

−4

)

2

×(10

4

−10

3

)×9.8

=20m/s

Velocity attained by the ball after descending h height from rest is given by

v

2

=2gh∵v

2

=u

2

=2aS

⇒h=

2g

v

2

⇒h=

2×9.8

20

2

=20.4m