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A spherical ball of radius 3xx10^(-4)m a...

A spherical ball of radius `3xx10^(-4)`m and density `10^(4)kg//m^(3)` falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h the viscosity of water is `9.8xx10^(-6)N-s//m^(2)`

A

`1.65xx10^(3)m`

B

`2.65xx10^(2)m`

C

`3.65xx10^(4)m`

D

`1.45xx10^(2) m`

Text Solution

Verified by Experts

The correct Answer is:
A
Before entering the water the velocity of ball is `sqrt(2gh)`. If after entering the water this velocity does not change, then this value should be equal to the terminal velocity. Therefore,
`sqrt(2gh)=(2)/(9)(r^(2)(rho-sigma)g)/(eta)`
`therefore h=({(2)/(9)(r^(2)(rho-sigma)g)/(eta)}^(2))/(2g)=(2)/(81)xx(r^(4)(rho-sigma)^(2)g)/eta^(2)`
`=(2)/(81)xx((3xx10^(-4))^(4)(10^(4)-10^(3))^(2)xx9.8)/((9.8xx10^(-6))^(2))=1.65xx10^(3)m`
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