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.
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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
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