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A ball of radius r and density r falls f...

A ball of radius r and density r falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is `eta` the value of h is given by
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A

`(2)/(9) r^(2)((l-rho)/(eta))g`

B

`(2)/(81)r^(2)((rho-1)/(eta))g`

C

`(2)/(81)r^(4)((rho -1)/(eta))^(2)g`

D

`(2)/(9)r^(4)((rho -1)/(eta))^(2)g`

Text Solution

Verified by Experts

The correct Answer is:
C
Velocity of ball when it strikes the water surface `v=sqrt(2gh)" "…..(i)`
Terminal velocity of ball inside the water `v=(2)/(9)r^(2)g((rho-1)/(eta))" "……(ii)`
Equating (i) and (ii) we get `sqrt(2gh)=(2)/(9) (r^(2)g)/(eta) (rho-1) implies h=(2)/(81) r^(4) ((rho-1)/(eta))^(2)g`
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