A40 cm. diameter sphere that weighs 400 n is released from rest underwater in claytor lake. its initial acceleration is about:

Newton's second law states that the resultant of the forces acting on the sphere is equal to the product between its mass m and its acceleration a:


There are two forces acting on the sphere: its weight W, directed downward, and the buoyancy B, directed upward. So Newton's second law becomes
(1)

We already know the weight of the sphere: , from which we can also find the mass of the sphere:


The buoyancy is equal to the mass of the water displaced:

where
is the water density
V is the volume of water displaced, which corresponds to the volume of the sphere, since the sphere is underwater
g is the gravitational acceleration
The radius of the sphere is
, so its volume is


So now we can rewrite Newton's second law (1) as

and solve it to find the acceleration of the sphere, a:


and this acceleration is directed downward, since it has the same sign of g.

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