Question

A wooden block of density $400kg{{m}^{-3}}$ immersed in water up to a depth d below the surface of water and then released. Calculate the acceleration of the ball inside the water.
$\begin{align}
  & a)10 \\
 & b)5 \\
 & c)15 \\
 & d)none \\
\end{align}$

Answer 1

Hint: Let us find out the net forces acting on the ball inside the water. Next, the net force acting on the ball is the buoyancy force acting in the upward direction and the weight of the ball acting downwards. The net force is equal to the product of mass and acceleration of the ball.
Formulas sued:
$F=ma$

Complete answer:
Let us assume the volume of the ball as v. Now, let us find the weight of the ball acting downwards,
$\begin{align}
  & W=mg \\
 & \Rightarrow W=400(V)g \\
\end{align}$
next, let us find the upward force, also called as buoyancy force and upthrust,
${{F}_{b}}=(1)Vg$
Now, the net force acting on the ball will be,
$\begin{align}
  & ma=mg-{{F}_{b}} \\
 & \Rightarrow 400Va=400Vg-Vg \\
 & \Rightarrow a=\dfrac{400g-g}{400} \\
 & \Rightarrow a=9.975m{{s}^{-2}} \\
 & \Rightarrow a\sim 10m{{s}^{-2}} \\
\end{align}$

Therefore, the correct option is option a.

Additional information:
Buoyancy force is the force exerted an object that is wholly or partly immersed in a liquid. Buoyancy acts upward for the kind of situations encountered in everyday experience. Buoyancy is caused by differences in pressure acting on opposite sides of an object immersed in a static fluid. Pressure variations in a fluid are typically caused by gravity, but in general buoyant forces act opposite to the direction of frame of reference acceleration. Under conditions of apparent weightlessness there can be no buoyant forces. Archimedes' principle says that the magnitude of the buoyant force on an object is equal to the weight of the fluid it displaces. The factors that affect buoyancy are the density of the fluid, volume of the fluid displaced, acceleration of gravity.

Note:
The buoyant force is not affected by mass of the immersed object, density of the immersed object. Buoyancy force depends on density of the liquid, volume of the object immersed in the liquid and the acceleration due to gravity. It doesn't depend on the density of the object.