Question

At a given place where acceleration due to gravity is $gm/se{c}^2$ , a sphere of lead of density $dkg/m^3$ is gently released in a column of liquid of density $\rho kg/m^3$ . If $d>\rho$, then immediately after the sphere is released inside the liquid, it will:

• A. fall vertically with an acceleration of $g$ $m/se{c}^2$
• 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 $\left(g\rho \right)/d$

Answer 1

Answer: (C)

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

$a=\frac{mg-F_B}{m}=\frac{\frac{4}{3}\pi r^{3}dg-\frac{4}{3}\pi r^3\rho g}{\frac{4}{3}\pi r^{3}d}$
$=\frac{(d-\rho )}{d}g$