Question

A rectangular block of wood of density 800kgm${}^{-3}$ having a mass of 2kg is pushed in to water so that it is completely submerged and then released. Neglecting viscous forces, the initial acceleration of the block will be (g $=$ 10 m/s${}^2$):

• A. $1.25m/s^2$ downward
• B. $2.5m/s^2$ upward
• C. $1.25m/s^2$ upward
• D. $2.5m/s^2$ downward

Answer 1

Answer: (B)

$2.5m/s^2$ upward

Here we have to use the concept of buoyancy force.

$Buoyancy$ $force$ = ($Volume$ $submerged$)($density$ $of$ $liquid$)($g$)

Force of buoyancy will act upwards on the body

$Volume$=$\frac{mass}{density}$=$\frac{1}{400}{m}^3$

By Newton's Second Law,

$mg-V\rho g=ma$
$\Rightarrow 2\times 10-\frac{2}{800}\times 1000\times 10=2a$

$a=-2.5m{s}^{-2}$

So the net acceleration is $2.5m{s}^{-2}$ $upwards.$