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)

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

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