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 $ ρ \,kg/m^3 $ . If $ d > ρ $ , the sphere will

• A. fall vertically with an acceleration $ g \,m/s2 $
• 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)

Apparent weight $=$ actual weight $-$ upthrust
$V d g^{'} =V d g-V \rho g $
$g^{'} =\left(\frac{d-\rho}{d}\right) g$