Question

Mass of stone=10 kg
relative density=4
Find the work done in lifting the stone through a height of 20m inside the lake

Answer 1

work done = apparent weight x height
here a=g=10m/s (take 10 m/s) height=20 m
(apparent weight taken because weight of stone seems to be decrease in water compared to air)
by archemedes principle,
apparent weight=original weight(stone) - weight of volume of water replaced by stone.

volume of water replaced = volume of stone.
given relative density=4=density of stone/density of water
=d/1000.
d=4000 kg/m^3
now, d=mass/volume.
volume,v=mass/d=10/4000=1/400 m^3.
mass of water replaced=density x volume=1000 x (1/400)= 2.5 kg.
weight of water replaced=mass x g=2.5*10=25 N
Apparent weight=10*10-25=75 N

work done=75*height=75*20=1500 N