in this example we are given that a tank containing
water of mass m, is placed on a weighing machine.
a stone of weight w is hung and loword in
water without touching the sides of the container
and if volume of stone is v, and density of
water is rho we are required to find what
will be the read-ing of weighing machine now.
in this situation we can say, as, water is
of total mass m , in this situation , when
, this stone is hung. we can simply state
in this situation.
water will, apply a buoyant force on the stone
in upward direction that will be f-b. and
according to newton’s third law the stone
will also exert the force f-b . on the water
in downward direction . so the total force
acting on the water will be, one is m-g in
downward direction and other is the buoyant
force acting on it in downward direction.
so we can simply state , the total force.
on weighing machine . is.
this total force we can simply write as mg
that is weight of water plus, the buoyant
force , and here buoyant force can be simply
, written as v rho g . as, the total volume
v is submerged and it is equal to the volume
of liquid displace.
so the total weight of liquid displaced is
v ro g. so in this situation we can directly,
write down the reading of weighing machine
. which can be written as reading of machine
in, kilogram force , can be given as simply
r. which is equal to mg + v ro g divided by
g, as this the value of , the force exerted
in newton , so this can be written as m +
v ro. that will be the answer to our problem
this is the total reading shown by the weighing
machine in kilogram force.
