Reading of weighing machine Consider the following situation:

The following ball is released and just after that reading of weighing machine is noted.
Now, it is given that Mass of container is $M$ and mass of liquid is $m$ and mass of ball is $m_0$.
Now, My professor said that if the density of ball is not equal to the density of liquid, then Reading of machine will be more than $(M + m + m_0)g$.
But according to me it will possible only if density of ball < density of water since reading of machine will be (M + m + density of water * Volume of ball)g
Am I somewhere wrong?
 A: I agree that the force measured on the scale will be as you stated:

(M + m + density of water * Volume of ball)g

If the ball < density of water it will experience a buoyancy force that will accelerate it upwards; providing the equal and opposite reaction. The acceleration of the ball upwards is not measured by the scale until viscus forces occur or the ball reaches the surface.
If the ball > density of water it will also experience the same boyancy force decelerating it; providing an equal and opposite reaction. The excess acceleration from gravity on the ball in freefall will not be measured by the scale until viscus forces occur or the ball strikes the bottom of the container.
A: Assuming an ideal liquid, the only way that there is communication between the liquid (and hence the balance) and the ball is via the "upthrust" - upward force on ball due to liquid and downward force on liquid due to ball.
Assume that the ball is held still in position under the liquid then there are three forces acting on the ball: weight downwards, upthrust upwards and another force which prevents the ball from moving, which result in a net zero force on the ball.
If the force which prevented the ball from moving is removed the ball now has a net force on it.
However, the forces on the liquid (and also the balance), including the downward force exerted by the ball are unchanged, so there is no change in the reading on the balance.
A: The center of mass of the system (container, fluid, and ball) is initially at rest.  When the ball is released, the center of the mass of the system will start moving downwards, i.e., it will be accelerating downwards.  This downward motion of the COM occurs both when the fluid is denser than the ball and when the ball denser than the fluid;  the only case in which the center of mass won't move is when the ball is neutrally buoyant.
Since the center of mass of the system is initially accelerating downwards, this means that there must be a net downwards force on the system.  This in turn means means that the normal force exerted by the scale is initially less than the weight of the system, not more;  and so the scale will register a weight less than the true weight of the system.
Once the ball has reached its terminal velocity downward (or upward) in the fluid, the COM of the system will be moving at constant velocity.  At that point the force of gravity and the normal force from the scale are again in balance, and so the weight registered on the scale will be the true weight of the system.  This will continue to hold until the ball breaks the surface or hits the bottom of the container.
