Question

At a given place where acceleration due to gravity is $gm/s^2$, a sphere of lead of density $dkg/m^3$ is gently released in a column of liquid of density $\rho kg/m^3$. If $d>\rho$, the sphere will :

• A. Fall vertically with an acceleration $gm/s^2$
• B. Fall vertically with no acceleration
• C. Fall vertically with an acceleration $g\left(\frac{d-\rho }{d}\right)$
• D. Fall vertically with an acceleration $g\left(\frac{\rho }{d}\right)$

Answer 1

Answer: (C)

Fall vertically with an acceleration $g\left(\frac{d-\rho }{d}\right)$

Let the volume of sphere be $V$.

So its mass is, $m=Vd$

When released in the liquid,

Gravitational force in downward direction is, $F_g=mg=Vdg$

Buoyancy force in the upward direction is, $F_b=V\rho g$

Net force on the sphere, $F_{net}=F_g-F_b=VG(d-\rho )$

So net acceleration is, $F_{net}/m=Vg(d-\rho )/Vd=g\left(\frac{d-\rho }{d}\right)$

Option C is correct.