A spherical ball of radius 1 mm and density 10 . 5 g cc - 1 is dropped in glycerine of coefficient of viscosity 9 . 8 poise and density 1 . 5 g cc - 1 . Viscous force on the ball when it attains const

Question

A spherical ball of radius 1 mm and density 10 . 5 g cc - 1 is dropped in glycerine of coefficient of viscosity 9 . 8 poise and density 1 . 5 g cc - 1 . Viscous force on the ball when it attains constant velocity is 3696 × 10 - x N . The value of x is (Given, g = 9 . 8 m s - 2 and π = 22 7 )

TestHub · Accepted Answer

Viscous force on the ball when it attains constant velocity i.e., terminal velocity is,

$F_{v} = (m g - F_{B}) (As, a = 0)$

Here, $F_{B}$ is buoyant force.

$\Rightarrow F_{v} = V ρ_{b} g - V ρ_{g} g = V g (ρ_{b} - ρ_{g}) = \frac{4}{3} π {(10^{- 3})}^{3} \times 9.8 [(10.5 - 1.5) \times 10^{3}] \approx 3696 \times 10^{- 7} N$

Thus, $x = 7$ .

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