Answer
A force of 1110 N would be needed to push the ball completely under the water.
Work Step by Step
We can find the volume of the beach ball as:
$V = \frac{4}{3}\pi~r^3$
$V = \frac{4}{3}\pi~(0.30~m)^3$
$V = 0.113~m^3$
Since the beach ball is very light, we can ignore the weight of the beach ball. The force $F$ we need to apply will be equal to the buoyant force $F_B$ on the ball. The buoyant force is equal to the weight of the water that is displaced by the ball's volume.
$F = F_B$
$F = \rho~V~g$
$F = (1000~kg/m^3)(0.113~m^3)(9.80~m/s^2)$
$F = 1110~N$
A force of 1110 N would be needed to push the ball completely under the water.
