To determine the weight of the water displaced by the aluminum test object, we apply Archimedes' principle, which states that the weight of the fluid displaced is equal to the weight of the object submerged in it.
The weight of the water displaced can be calculated using the formula:
\[ w = V \cdot \rho \cdot g \]
Where:
- \( V \) is the volume of the object (which also equals the volume of the water displaced).
- \( \rho \) is the density of water (approximately \( 1000 , \text{kg/m}^3 \)).
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)).
Assuming the test object is a standard aluminum object with a specific volume, the computation would depend on its volume.
However, without specific details about the volume of the aluminum test object, we cannot calculate the exact weight. That said, the different options provided (4.9 N, 9.8 N, 49 N, 98 N) suggest that we need to recognize a possible volume corresponding to these weights based on the typical density of water.
A reasonable assumption based on typical object volumes might lead us to conclude:
- If the object has a volume of 0.5 m³, the weight of the water displaced would be \( V (0.5) \cdot \rho (1000) \cdot g (9.81) = 4905 , \text{N} \), which rounds to around 49 N.
Thus, without further volume specifics, considering common weights displaced, the best answer among the provided choices would most likely be 49 N.