A small ball of mass m and density is dropped in a viscous liquid of density ?. After some time, the ball falls with constant velocity. The viscous force on the ball is:

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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 constant velocity. The viscous force on the ball is: [2024]

1 $m g (\frac{ρ_{0}}{ρ} - 1)$

2 $m g (1 - ρ ρ_{0})$

3 $m g (1 - \frac{ρ}{ρ_{0}})$

4 $m g (1 - \frac{ρ_{0}}{ρ})$

Ans.
(4)

At constant velocity, $F_{v} + F_{B} = m g$

$F_{B} = ρ_{0 \cdot} (\frac{m}{ρ}) \cdot g$

$F_{v} = m g - F_{B} = m g - \frac{m}{ρ} ρ_{0} g \Rightarrow F_{v} = m g (1 - \frac{ρ_{0}}{ρ})$

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 constant velocity. The viscous force on the ball is: [2024]

1 $m g (\frac{ρ_{0}}{ρ} - 1)$

2 $m g (1 - ρ ρ_{0})$

3 $m g (1 - \frac{ρ}{ρ_{0}})$

4 $m g (1 - \frac{ρ_{0}}{ρ})$

Ans.
(4)

At constant velocity, $F_{v} + F_{B} = m g$

$F_{B} = ρ_{0 \cdot} (\frac{m}{ρ}) \cdot g$

$F_{v} = m g - F_{B} = m g - \frac{m}{ρ} ρ_{0} g \Rightarrow F_{v} = m g (1 - \frac{ρ_{0}}{ρ})$

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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 constant velocity. The viscous force on the ball is: [2024]

1 mg(ρ0ρ-1)

2 mg(1-ρρ0)

3 mg(1-ρρ0)

4 mg(1-ρ0ρ)

Ans. (4) At constant velocity, Fv+FB=mg FB=ρ0·(mρ)·g Fv=mg-FB=mg-mρρ0g⇒Fv=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 constant velocity. The viscous force on the ball is: [2024]

1 $m g (\frac{ρ_{0}}{ρ} - 1)$

2 $m g (1 - ρ ρ_{0})$

3 $m g (1 - \frac{ρ}{ρ_{0}})$

4 $m g (1 - \frac{ρ_{0}}{ρ})$

Ans.
(4)

At constant velocity, $F_{v} + F_{B} = m g$

$F_{B} = ρ_{0 \cdot} (\frac{m}{ρ}) \cdot g$

$F_{v} = m g - F_{B} = m g - \frac{m}{ρ} ρ_{0} g \Rightarrow F_{v} = m g (1 - \frac{ρ_{0}}{ρ})$