IMAT 2019 Q55 [Stone Upthrust]

A stone of density 5.20 g / cm^3 and volume 200 cm^3 is completely submerged in a liquid of density 1.20 g / cm^3.
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What is the magnitude of the upthrust acting on the stone?

[gravitational field strength = 10.0 N / kg]

A. 6.40 N
B. 2.00 N
C. 10.4 N
D. 8.00 N
E. 2.40 N

The upthrust force is produced or performed by the liquid. As per it’s density we will be able to see how much force it exerts onto the stone.

If the liquid takes 1.20 g for every 1 cm^3, then it should be able to withstand 240 g for the 200 cm^3 of the liquid.

We should now convert this mass into weight, first by converting it Kg’s and then into Newtons.

240g= 0.24 Kg

10N for every 1 kg means that for 0.24 Kg we have 2.4N.

We can therefore conclude the liquid exerts an upwards force of 2.4 N onto the stone- and our answer is E.