Question

A piece of wood is taken deep inside a long column of water and released, it will move up

• A. With a constant upward acceleration
• B. With a decreasing upward acceleration
• C. With a decelaration
• D. With a uniform velocity

Answer 1

The correct option is B

With a decreasing upward acceleration

The net upward force at any moment upon the block can be given as,
$F_{net}=F_B-F_V-mg$
Where, $F_B$ = Force of Bouancy, upwards
$F_v$ = Viscous force, downwards
mg = weight, downwards

$\Rightarrow F_B-F_v-mg=ma$
a = acceleration of the block
But initially, v=0$\Rightarrow F_v=0$
As,$|F_v|=6\pi \eta rv$

As velocity increases.$F_v$ also increases. it shows clearly that the net acceleration is maximum initially and reduces as $F_v$ increases.