A small ball of mass M and density is dropped in a viscous liquid of density . After some time, the ball falls with a constant velocity. What is the viscous force on the ball? [2023]

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Q.
A small ball of mass M and density $ρ$ is dropped in a viscous liquid of density $ρ_{0}$ . After some time, the ball falls with a constant velocity. What is the viscous force on the ball [2023]

1 $F = M g (1 - \frac{ρ_{0}}{ρ})$

2 $F = M g (1 + \frac{ρ}{ρ_{0}})$

3 $F = M g (1 + ρ ρ_{0})$

4 $F = M g (1 + \frac{ρ_{0}}{ρ})$

Ans.
(1)

$For constant velocity F_{net} = 0$

$F_{vis} + ρ_{0} v g = ρ v g$

$F_{vis} = (ρ - ρ_{0}) v g$

$= ρ v g (1 - \frac{ρ_{0}}{ρ}) = M g (1 - \frac{ρ_{0}}{ρ})$

Solution

Q.
A small ball of mass M and density $ρ$ is dropped in a viscous liquid of density $ρ_{0}$ . After some time, the ball falls with a constant velocity. What is the viscous force on the ball [2023]

1 $F = M g (1 - \frac{ρ_{0}}{ρ})$

2 $F = M g (1 + \frac{ρ}{ρ_{0}})$

3 $F = M g (1 + ρ ρ_{0})$

4 $F = M g (1 + \frac{ρ_{0}}{ρ})$

Ans.
(1)

$For constant velocity F_{net} = 0$

$F_{vis} + ρ_{0} v g = ρ v g$

$F_{vis} = (ρ - ρ_{0}) v g$

$= ρ v g (1 - \frac{ρ_{0}}{ρ}) = M g (1 - \frac{ρ_{0}}{ρ})$

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Solution

Q. A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ0. After some time, the ball falls with a constant velocity. What is the viscous force on the ball [2023]

1 F=Mg(1-ρ0ρ)

2 F=Mg(1+ρρ0)

3 F=Mg(1+ρρ0)

4 F=Mg(1+ρ0ρ)

Ans. (1) For constant velocity Fnet=0 Fvis+ρ0vg=ρvg Fvis=(ρ-ρ0)vg =ρvg(1-ρ0ρ)=Mg(1-ρ0ρ)

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Q.
A small ball of mass M and density $ρ$ is dropped in a viscous liquid of density $ρ_{0}$ . After some time, the ball falls with a constant velocity. What is the viscous force on the ball [2023]

1 $F = M g (1 - \frac{ρ_{0}}{ρ})$

2 $F = M g (1 + \frac{ρ}{ρ_{0}})$

3 $F = M g (1 + ρ ρ_{0})$

4 $F = M g (1 + \frac{ρ_{0}}{ρ})$

Ans.
(1)

$For constant velocity F_{net} = 0$

$F_{vis} + ρ_{0} v g = ρ v g$

$F_{vis} = (ρ - ρ_{0}) v g$

$= ρ v g (1 - \frac{ρ_{0}}{ρ}) = M g (1 - \frac{ρ_{0}}{ρ})$