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A metal ball ofradius 10^(-4) m and dens...

A metal ball ofradius `10^(-4)` m and density `10^4 kg//m^3` falls freely under gravity through a distance 'h' and enters a tank of water. It is found that after entering the water, the velocity of ball does not change. What is the value of h?
`[eta "for water "10^(-5)" Pas ",g=10m//s^2" and "orh_("water")=10^3kg//m^3`]

A

10m

B

15m

C

18m

D

20m

Text Solution

Verified by Experts

The correct Answer is:
D
When the ball falls through a vertical height h, it acquires the velocity v`=sqrt(2gh)" "[v^2=u^2+2gh]`
and since this velocity does not change, when the ball travels through water, it must be its terminal velocity or critical velocity`(v_c)=sqrt(2gh)`
It is given by `v_c=2/9(r^2(rho-sigma)g)/(eta)`
`:." "sqrt(2gh)=(2r^2)/(9)((rho-sigma)g)/(eta)`
`:." "h=[(2r^2)/(9)((rho-sigma)g)/(eta)]^2xx1/(2g)`
`=[(2xx(10^(-4))^2xx(10^(+4)-10^(+3))xx10)/(9xx10^(-5))]^2xx1/(20)`
`=[(2xx10^(-8)xx9xx10^3xx10^1xx10^5)/(9)]^2xx1/(20)`
`:." "h=(20xx20)/(20)=20m`
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