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# 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}

Last updated date: 15th Aug 2024
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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:
$F=ma$

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.