in this example we are given that a piece
of alloy of mass 96 gram is composed of two
metals.
whose specific gravity are 11 point 4 and
seven point 4 respectively.
if the weight of alloy is 86 gram, in water
that means it is 86 gram when weight in water,
we are required to find the mass of each metal
in the alloy. and very first thing we can
say, let.
mass of.
first metal . in alloy. is, x. say if it is
x. then we can directly state . that of.
second metal.
is.
total mass is 96 gram for the first metal
if it is x it can be written as 96 minus x.
and obviously we are taking it in grams. and
when it is weight in water we know that.
weight in water can be directly written as.
actual weight.
minus.
force of buoyancy. as only due to the force
of buoyancy the weight is reduced what we
call apparent weight . now weight in water
is given as 86 this is equal to 96 minus,
the total buoyancy force, and if we talk about
force of buoyancy that can be written as . say
for the first metal its mass is x. then its
volume can be written as, x divided by its
specific gravity is 11 point four, multiplied
by specific gravity for water which is relative
density only so it can be taken as one . minus
for 96 minus x gram of second metal where
specific gravity is 7 point 4 it can be written
as 96 minus x by , 7 point 4 into one.
now for this expression if we solve.
we can directly write solving we get, if i
just numerically simplify the expression i’ll
get the value of x to be , 62 point 7 gram.
this is the weight of metal one, in the alloy
, and for metal two we can simply state it
is 96 minus x so . 96 minus 62 point seven
can be written as, directly 33 point 3 gram
. this is the mass of, metal two in alloy
and that will be the answer to this problem.
