With a wooden ball and a high water tank we hold four experiments. In the first experiment we have a floating ball weighed in a vessel. In the second experiment, the ball is weighed while tied to the

Question

With a wooden ball and a high water tank we hold four experiments. In the first experiment we have a floating ball weighed in a vessel. In the second experiment, the ball is weighed while tied to the bottom of the vessel; the third time, the ball is held under water by a thin rod; finally, during the fourth experiment the ball is taken deep inside and released. In all four cases, the weight is recorded. In which case is the recorded weight more than the weight of the ball, water and tank?

TestHub · Accepted Answer

In C, the submerged wooden ball is held down by a rod supported outside the tank.
$F_{B} = ρ_{w} V g > m g$
For the ball at rest:
$F_{B} = m g + T$
$T = F_{B} - m g > 0$
The ball pushes the water downward by its buoyant force. The scale therefore reads:
$W_{scale} = W_{tank + water} + F_{B}$
$W_{scale} > W_{tank + water} + m g$
Thus C reads more than the total weight of the tank, water and ball.

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