Question

A sphere falls from rest into water from a height of $2m$. The relative density of the sphere is $0.80$. Find the depth to which the sphere will sink (in metres).

Answer 1

Velocity of ball/sphere at time of entering water, $v=\sqrt{2gh}$

$\Rightarrow V=\sqrt{2\times 10\times 9}$

$V=2\sqrt{10}m/s$

Now, in water, buoyancy exerts-

$\Rightarrow f_0=mg$

$\Rightarrow {\rho }_f{v}_{b}a={\rho }_b{v}_{10}g$

$\Rightarrow a\times 0.8{\rho }_b={\rho }_b\left(10\right)$

$\Rightarrow a=12.5m/s^2$

Net deacceleration $=(12.5-10)m/s^2$

$=2.5m/s^2$

now, $v^2=u^2-2ab$

$\Rightarrow s=\frac{u^2}{2a}=\frac{8\times 5}{2\times 2.5}$

$s=8m$

Hence, the answer is $8m.$