Question

A body and density $\rho$ is sinking in a fluid of density ${\rho }_o$. Its acceleration is given by

• A. $g(1-\frac{\rho }{{\rho }_o})$
• B. $g(1+\frac{{\rho }_o}{\rho })$
• C. $g(1-\frac{{\rho }_o}{\rho })$
• D. $g(1+\frac{\rho }{{\rho }_o})$

Answer 1

Answer: (C)

$g(1-\frac{{\rho }_o}{\rho })$

Let volume of body be $V$

Total Force on body = Weight of body - upthrust

$=\rho Vg-{\rho }_{o}Vg$ ..........(1)

By newton's second law,

Force = ma

$=\rho Va$ ............(2)

From (1) and (2),

$\rho Va=\rho Vg-{\rho }_{o}Vg$

$a=g(1-{\rho }_o/\rho )$