First slide

Pressure in a fluid-mechanical properties of fluids

Question

A ball whose density is 0.4 x 10³ kg/m³ falls into water from a height of 9 cm . To what depth does the ball sink?

Moderate

A

9 cm
B

6 cm
C

4.5 cm
D

2.25 cm

Solution

The velocity of ball before entering the water surface:
$v = \sqrt{2 g h} = \sqrt{2 g \times 9}$
When ball enters into water, due to the upthrust of water, the velocity of ball decreases (or retarded).
$Retardation, a = \frac{Apparent weight}{Mass of ball}$
$= \frac{V (ρ - σ) g}{V ρ} = (\frac{ρ - σ}{ρ}) g = (\frac{0.4 - 1}{0.4}) \times g = - \frac{3}{2} g$
lf h be the depth up to which the ball sinks. Then
$\begin{array}{rcl} 0 - v^{2} & = & 2 \times (- \frac{3}{2} g) \times h \Rightarrow 2 g \times 9 = 3 g h \\ ∴ h & = & 6 cm \end{array}$

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