In this illustration we'll be analyzing 2
spheres connected with a string.
we are given that 2 solid uniform spheres
each of radius 5 centimeter are connected
by a light string, and in a tank of water.
it is saying if specific gravities of submerged
spheres are point 5 and 2. then obviously
the heavier 1 would be, lower 1, and the lighter
1 will be upper 1. we are required to find
the tension in the string and the contact
force between the bottom of tank and the heavier
sphere.
so here, we can directly write down, for,
equilibrium. of, lighter sphere. here for
this lighter sphere if we just have a look
on its free body diagram it'll be experiencing
in downward direction.
a tension, plus, its weight we can write at
its volume multiplied by, the density is point
5 times ro of water multiplied by g. and upward
direction is the buoyant force acting on it
which is v. ro of water, multiplied by g.
so, in this situation here we can write for
this lighter sphere t, plus, v times zero
point 5 ro water multiplied by g to be equal
to v ro water, g. now, in this situation,
here we calculate the value of tension we
are getting the value of tension is equal
to v ro water g by 2. and in this situation,
we can get the volume by using the radius
as 4 by 3.
pie zero point zero, 5, cube. multiplied by,
water density to be taken as thousand g as
10.
whole divided by 2.
numerically when we solve it this gives us
2 point 5 6 5 newton that is 1 result of this
problem.
similarly if we calculate for.
equilibrium, of.
heavier sphere. here, we can again draw its
free body diagram where it'll be experiencing
a tension in upward direction.
normal reaction in upward direction and buoyant
force that is, v ro water g in upward direction
and downward direction it is only experiencing
its weight.
which is v multiplied by twice of ro water
g. now for balancing, the forces on it we
can write t plus, n, plus v. ro water g should
be equal to v times 2 ro water g. so in this
situation, the value of normal reaction here
will get is, this will be equal to.
v, ro water g. minus, the normal reaction.
so if you calculate the value of v ro water
g this we have calculated over here, this
is 5 point 1 3 newton minus the normal reaction
is 2 point, 5 6 5 newton numerically, the,
tension.
this is tension, rather then i have taken
normal reaction.
so this will be also 2 point 5 6 5 newton,
that will be the result of this problem.
