A beaker weighing $2.0\,\text{N}$ is filled with $5.0 \times 10^{-3}\,\text{m}^3$ of water. A rubber ball weighing $3.0\,\text{N}$ is held entirely underwater by a massless string attached to the bottom of the beaker, as represented in the figure above. The tension in the string is $4.0\,\text{N}$. The water fills the beaker to a depth of $0.20\,\text{m}$. Water has a density of $1000\,\text{kg/m}^3$. The effects of atmospheric pressure may be neglected.

Question

A beaker weighing $2.0\,\text{N}$ is filled with $5.0 \times 10^{-3}\,\text{m}^3$ of water. A rubber ball weighing $3.0\,\text{N}$ is held entirely underwater by a massless string attached to the bottom of the beaker, as represented in the figure above. The tension in the string is $4.0\,\text{N}$. The water fills the beaker to a depth of $0.20\,\text{m}$. Water has a density of $1000\,\text{kg/m}^3$. The effects of atmospheric pressure may be neglected.(a) Calculate the weight of the entire apparatus.
, (b) Draw and label the forces (not components) that act on the ball.
, (c) Calculate the buoyant force exerted on the ball by the water.
, (d) Calculate the pressure due to the liquid (the gauge pressure) at the bottom of the beaker.
, (e) The string is cut, and the ball rises to the surface and floats. Indicate whether the water level is higher, lower, or the same after equilibrium is reached. Justify your answer.
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Jason · Accepted Answer

$5.4\times10^{1}\,\text{N}$
$W\,\text{down},\;T\,\text{down},\;B\,\text{up}$
$7.0\,\text{N}$
$2.0\times10^{3}\,\text{Pa}$
$\text{lower}$

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