Class 11

Physics

Mechanics

Mechanical Properties of Fluids

If ball of steel (density $ρ=7.8cm_{−3}$) attains a terminal velocity of $10cms_{−1}$ when falling in a tank of water (coefficient of viscosity $η_{water}=8.5×10_{−4}Pa.s$) then its terminal velocity in glycerin ($ρ=1.2gcm_{−3}η=13.2Pa.s$) would be nearly:

- $1.5×10_{−5}cms_{−1}$
- $1.6×10_{−5}cms_{−1}$
- $6.25×10_{−4}cms_{−1}$
- $6.45×10_{−4}cms_{−1}$

$(ρ_{b}−ρ_{l})Vg=6πηrv$...eq(1)

1. case

when ball falling in tank of water of density $ρ_{water}=1gcm_{−3}$, $ρ_{ball}=7.8gcm_{−3}$$η_{water}=8.5×10_{−4}Pa.s$ and terminal velocity $v=10cms_{−1}$

Put all the above value in eq(1)

$⇒(7.8−1)Vg=6π×8.5×10_{−4}r×10$...eq(2)

2. case

when ball falling in tank of glycerin

$ρ_{ball}=7.8gcm_{−3}$$η_{glycerin}=13.2Pa.s$ and terminal velocity $v_{1}$

put all the value in eq(1)

$⇒(7.8−1.2)Vg=6π×13.2r×v_{1}$...eq(3)

divide eq(3) b eq(1)

$7.8−17.8−1.2 =8.5×10_{−4}×1013.2×v_{1} $

$⇒v_{1}=6.8×13.26.6×8.510_{−4}×10 =6.25×10_{−4}cms_{−1}$

terminal velocity of ball in glycerin is $6.25×10_{−4}cms_{−1}$

Hence C option is correct.