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Bulk Modulus

A spherical b...

Question

A spherical ball of density $ρ$ is gently released in a liquid of density $σ (ρ > σ)$ . Find the initial acceleration of the ball.

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Solution

Let the volume of the ball be $V$ .
Mass of the ball $m = ρ V$
Buoyancy acting on ball $B = σ V g$
So, using $m a = m g - B$
Or $ρ V a = ρ V g - σ V g$
$⟹ a = g - \frac{σ}{ρ} g$

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