First slide

Fluid statics

Question

A ball whose density is $0.4 \times 10^{3} kg / m^{3}$ 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 $v = \sqrt{2 gh} = \sqrt{2 g \times 9}$
When ball enters into water, due to upthrust of water the velocity of ball decreases (or retarded)
The retardation, a = $\frac{apparent weight}{mass of ball}$
= $\frac{V (ρ - σ) g}{Vρ} = (\frac{ρ - σ}{ρ}) g$
= $(\frac{0.4 - 1}{0.4}) \times g = - \frac{3}{2} g$
If h be the depth upto which ball sink, then,
$0 - v^{2} = 2 \times (- \frac{3}{2} g) \times h$
$\Rightarrow 2 g \times 9 = 3 gh ∴ h = 6 cm$

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