Question

At a given place where , acceleration due to gravity is of g $m/s^2$, a sphere of lead o density $dkg/m^3$ is gently released in column of liquid of density $\rho$ kg/m3. If $d>\rho$ the sphere will

• A. fall vertically with an acceleration of g
• B. fall vertically with no acceleration
• C. fall vertically with an acceleration $g\left(\frac{d-p}{d}\right)$
• D. fall vertically with an acceleration $g\frac{p}{d}$

Answer 1

Answer: (C)

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

When a sphere of mass $m$ is released in a liquid , it falls vertically down with acceleration
$\frac{mg-F_B}{m}=\frac{\frac{4}{3}\pi r^{3}dg-\frac{4}{3}\pi r^{3}pg}{\frac{4}{3}\pi r^{3}d}$
$=\frac{(d-p)g}{d}$