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Puzzle for Today

Puzzle No. 316 – Wednesday 19 September

I'm doing the washing up and a 400 millilitre empty glass jar is floating in the water. The jar itself weighs 300 grams when empty. How much water do I need to pour into the floating jar to make it sink? Assume that the density of glass is three times the density of water.

Today’s #PuzzleForToday has been set by Dr Hugh Hunt, Reader in Engineering Dynamics and Vibration at Trinity College, Cambridge

If you assume that glass is infinitely dense, ie occupies zero volume, then the jar displaces 400ml of water and the upwards buoyancy force when the jar is on the verge of sinking is 400 grams. That means that only 100 grams of water is needed in addition to the weight of the jar to make it sink.

But the density of glass is 3 times that of water, so the volume of the 300g jar is 100ml and displaces an extra 100 grams of water, The total buoyancy force on the verge of sinking is therefore 500g. Hence 200g of water is needed for sinking.

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