An helicopter lowers a probe into lake Chad which is suspended on a cable. the probe has a mass of 500kg and its average density is 1400kg/m³. what is the tension in the cable?

Explanation:

If the mass of the probe is 500kg, its weight W = mass  acceleration due to gravity.

Weight of the probe = 500*9.81

Weight of the probe = 4,905N

If its average density =  1400kg/m³

Volume = Mass/Density

Volume = 500/1400

Volume = 0.3571m³

According to the floatation principle, the volume of the probe is equal to the volume of liquid displaced. Hence the volume of water displaced is 0.357m³.

Since density of water is 1000kg/m³, we can find the mass of the water using the formula;

Mass of water = Density of water * Volume of water

Mass of water = 1000*0.3571

Mass of water = 357.1kg

Weight of water displaced = 3571 * 9.81 = 3503.15N

The tension in the cable will be the difference between the weight of the probe and weight of the displaced fluid.

Tension in the cable = 4,905N -  3503.15N

Tension in the cable = 1,401.85N

Hence the tension in the cable is 1,401.85N

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