in this example we are given that an open
u-tube of uniform cross section contains some
mercury. and it is saying when 40 point 8
centimeter length of water is poured in one
arm of u tube. we are required to find how
high does the mercury rise in other arm from
initial level.
and the densities also given to us.
here we can draw the physical situation that,
if this is the u tube . say in the left arm
this 40 point 8 centimeter length of water
is poured.
we can simply state due to , this water mercury
will be pushed down.
And, mercury level on the other side will
be slightly raise.
and the situation would be like this.
now in this situation earlier , say mercury
level.
was. at this value.
and after pouring the water in one side , the
lefthand side mercury level will go down by
h and the righthand side it will rise up by
h. and we are require to find how high is
the mercury , rise in other arm from its initial
level so we need to find h. however level
difference on the two arms of u tube is two
h. and in this situation if we draw a horizontal
level.
with points ay and b in the mercury, ay is
at the interface of water and mercury and
b is in the mercury. we can simply state the
level of mercury on the other arm will be
two h above the point b. and we are given
that this water, column is of height , 40
point 8 centimeter . so we can directly write
in final state, we have.
here we can simply write pressure at point
ay must be equal to pressure at point b. if
we substitute the values pressure at point
ay can directly be written as p- atmospheric
, plus 40 point 8 multiplied by one into g.
this h ro g due to the, water column of height
40 point 8 centimeter this equal to if we
find out the pressure at b. it can be written
as p-atmospheric plus, 2 h multiplied by , the
density of mercury is 13 point 6 into g. here
p-atmospheric gets cancelled out. and g also
gets cancelled out.
so in this situation the value of h can be
directly given as 40 point 8 divided by two
into 13 point 6. on simplifying directly we’ll
get the value to be 1 point 5centimeter that
is the answer to our problem.
