Question

If the acceleration due to gravity is $gm{s}^{-2}$, a sphere of lead of density $\delta kg/m^3$ is gently released in a column of liquid of density $dkg/m^3(\delta >d)$, the sphere will fall vertically with:

• A. an accleration of $8m/s^2$.
• B. no acceleration.
• C. an accleration of $g[1-\frac{d}{\delta }]m/s^2$.
• D. an acceleration $g\left(\frac{\delta }{d}\right)$ $m/s^2$.

Answer 1

The correct option is C an accleration of $g[1-\frac{d}{\delta }]m/s^2$.

Force due to gravity $=Vg\delta$
Where V is the Volume of the Sphere , $\delta$ is the density of the sphere and g is the acceleration due to gravity .
Force due to buoyancy $=Vgd$ where d is the density of the liquid .
Net Force $=Vg(\delta -d)$
$\therefore$ Net acceleration $=\frac{Vg(\delta -d)}{V\delta }=g(1-\frac{d}{\delta })$