A spherical ball of radius 1 mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. The viscous force on the ball when it attains constant velocity is . The value of is. (Given: and ) ________ .

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Solution

Q.
A spherical ball of radius 1 mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. The viscous force on the ball when it attains constant velocity is $3696 \times 10^{- x} N$ . The value of $x$ is. (Given: $g = 9.8 {m/s}^{2}$ and $π = \frac{22}{7}$ ) ________ . [2023]

Ans.
(7)

$When the ball attains terminal velocity$

$F_{v} = (m g - F_{B}) (∵ a = 0)$

$= V σ_{b} g - V ρ_{ℓ} g = V (σ_{b} - ρ_{ℓ})$

$= \frac{4}{3} π {(10^{- 3})}^{3} \times 9.8 (10.5 - 1.5) \times 10^{3}$

$= 3696 \times 10^{- 7} N$

$So, x = 7$

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