What is the depth to which the block is submerged?

Question

A rectangular block of base dimensions #20cm*20cm# and weighs 50 Newtons, floats in water. Calculate the depth to which it is submerged given that the density of water is #1000kgm^-3#.

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Answer 1 · 2017-09-01T03:47:13

Let the depth to which the block is submerged be #x# cm.

The base area of the block #=20xx20cm^2#

So volume of the block submerged will be #V=20xx20xx xcm^3#

#=400x xx10^-6m^3#

So weight of water displaced by the block
#W=Vm^3xx1000kgm^-3xxg# N, where acceleration due to gravity #g=10m"/"s^2#

Given that the weight of the block is 50 N ,

By condition of floatation we get

#Vxx1000xxg=50#

#=>400x xx10^-6xx1000xx10=50#

#=>x=50/4=12.5cm#