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A steel ball of radius 0.5 xx 10^(-2)m ...

A steel ball of radius `0.5 xx 10^(-2)m` is dropped in a long jar containing olive oil of coefficient of viscosity `84 xx 10^(-3)Nsm^(-2)` and density `920kgm^(-3)`. If the density of the solid ball is `7.8 xx 10^(3)kgm^(-3)` then calculate the terminal velocity attained by the steel ball.

Text Solution

Verified by Experts

Given `r=5 xx 10^(-3)m" "h=8.4 xx 10^(-2) Nsm^(-2)" "sigma=9.2 xx 10^(2) kgm^(-3)`
`r=7.8 xx 19^(3)kgm^(-3)" "g=9.8 xx ms^(-2)`
We know that terminal velocity `=2/9 (r^(2)g)/(eta) (rho-sigma)`
`i.e, v_(t)=2/9 xx ((5 xx 10^(-3))^(2)xx 9.8 )/(8.4 xx 10^(-2)) (7.8 -0.92) xx 10^(3)=44.59 xx 10^(-1)=4.459 ms^(-1)`
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Knowledge Check

  • The young's modulus of steel is 20 xx 10^(10) N/ m^(2) . If the density of steel is 7.7 xx10^(3) kg/ m^(2) , the velocity of longitudinal wave in steel is nearly :

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    `1 xx 10^(2) ms^(-1)`
    B
    `1.56 xx 10^(-2) ms^(-1)`
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