Question

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 ?

Answer 1

(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/cm² .