in this example we are given that a rubber
ball of mass m and radius r is submerged.
in water to a depth h. and on releasing the
ball we are require to find to what height
above the water surface ball will jump. and
we are given that , we can neglect the resistance
of water and density of water is ro-w. in
this situation if we just draw physical situation
you can say this is the water level , and
from a depth h , a rubber ball is released.
then obviously when it’ll reach the surface
it’ll gain some ki-netic energy , and further
say it is raised up to a height h-one till
its final velocity becomes zero. now from
the initial point to the final point we can
see , its initial ki-netic energy was zero
and final ki-netic energy was also zero , so
we can directly apply the work energy theorem
, from initial state to the final state, as,
it is going up we can state . when it is inside
water it was acted upon by the buoyant force
. and the value of buoyant force can be simply
written as four by three pie r cube. which
is , the volume of ball multiplied by density
of water into g. v ro g. so in this situation,
we can directly use from , points i to f . using
work energy theorem . we get. here initial
ki-netic energy of the ball was zero. when
it is raised from starting to final point,
work done by buoyant force on it can be written
as f-b multiplied by h, as buoyant force is
constant, so it is acting up to a height h
only, outside no buoyant force is their. and
another force acting on the ball from starting
to final point is the gravity . so it can
be written as, minus mg total height is h
plus h one which can be taken as. zero. so
in this situation if we just reanalyze it
the value of h one the height up to which
the ball can be raise. is given by buoyant
force minus mg, divided by mg multiplied by
h this is the expression we use. buoyant force
value we can easily substitute here, so the
total height can be calculated as four by
three, pie r cube ro w , g can be cancelled
, minus m upon m. whole multiplied by h . this
will be the answer to this problem.
