Question

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

• A. fall vertically with an acceleration g $m/s^2$
• B. fall vertically with no acceleration
• C. fall vertically with an acceleration g $\frac{d-p}{d}$
• D. fall vertically with an acceleration g $\frac{p}{d}$

Answer 1

The correct option is C fall vertically with an acceleration g $\frac{d-p}{d}$

Apparent weight = actual weight upthrust
$\Rightarrow Vd{g}^{\prime }=Vdg-Vpg$
$\Rightarrow g^{\prime }=\frac{d-p}{d}g$