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A metal block of volume 1 * 10^3 cm^3 is suspended from a thread as shown in the diagram. It is lowered into a beaker of liquid of unknown density until it is completely immersed but does not touch the bottom of the beaker. The beaker rests on a balance. The reading of the balance before the block is lowered in the liquid is 4.00 kg, and is 5.8 after the block is completely immersed in the liquid. The volume and mass of the thread may be neglected in all the following calculations
The density of the liquid is:

Question 2 options:
A) 9.8 x 103 kg/m3

B) 4.0 x 103 kg/cm3

C) 1.8 x 103 kg/m3

D) 5.8 x 103 kg/m3

If the thread is released so that the block sinks to the bottom of the beaker and rests there, then the pan balance reads 12 kg. The density of the material from which the block is made is:

Question 3 options:
A) 6.2 x 103 kg/m3

B) 1.2 x 103 kg/cm3

C) 5.8 x 103 kg/m3

D) 8.0 x 103 kg/m3

You know the increase in the balance is equal to bouyancy, or 1.8kg

but bouyancy is equal to the density of the liquid*volume displaced, so set them equal, and I think the density then must be equal to 1.8kg/1000cm^3, that converts to one of the answers.

in the last part, you know the total mass of the weight must be 8kg, and you know its volume, figure denstiy