Question

A wooden ball of density $D$ is immersed in water of density $d$ to a depth h below the surface of water. Up to which height will the ball jump out of water, when it is released?

• A. $\frac{d}{D}h$
• B. $\left(\frac{d}{D}-1\right)h$
• C. $h$
• D. Zero

Answer 1

Answer: (B)

$W=\Delta k$
$(d-D)Vgh=\frac{1}{2}m{v}^2$
$(d-D)Vgh=\frac{1}{2}(DV)v^2$
$v^2=2gh\left(\frac{d-D}{D}\right)$

To reach maximum height from the free surface, this velocity
$v^2=2gH$
$2gh\left(\frac{d-D}{D}\right)=2gH$
$H=h\left(\frac{d}{D}-1\right)$