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A cubical block of wood 10 cm on a side and of density 0.5 g/cm3 floats in a jar of water. Oil of density 0.8 g/cm3 is poured on the water until the top of the oil layer is 4 cm below the top of the block. 

(a)  How deep is the oil layer ?

(b) What is the gauge pressure at the lower face of the block ?

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(a) Let the oil layer be x cm deep. Then weight of block = weight of oil displaced + weight of water displaced.

or (103 )(0.5) = 102 (x) (0.8) g + 102 (6 – x) 1

or x = 5 cm.

(b) Gauge pressure at the lower face of the block

= 5 × 0.8 × 98 + 1 × 1 × 980

= 4900 dynes/cm.

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