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A small ball of mass m and density is dropped in a viscous li

Question

A small ball of mass m and density $ρ$ is dropped in a viscous liquid having a density $ρ_{0}$ . After some time, the ball falls with a constant velocity. Calculate viscous force acting on the ball.

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A small ball of mass m and density

ρ

is dropped in a viscous liquid having a density

ρ_{0}

. After some time, the ball falls with a constant velocity. Calculate viscous force acting on the ball.

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Volume of the ball,

v = m / ρ

; a mass of liquid displaced by the ball.

m' = (\frac{m}{ρ}) ρ_{0}

ρ

= density of ball
When the ball falls with a constant velocity
⇒ viscous force = effective weight of the ball or

F = m g = m ’ g = (m - m ’) g

= (m - \frac{m ρ _{0}}{ρ}) g = m g (1 - \frac{ρ _{0}}{ρ})

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Question Text	A small ball of mass m and density $ρ$ is dropped in a viscous liquid having a density $ρ_{0}$ . After some time, the ball falls with a constant velocity. Calculate viscous force acting on the ball.
Answer Type	Text solution:1
Upvotes	151