Question

At a given place where acceleration due to gravity is ' $8^{\prime }\mathrm{m}/{\mathrm{s}}^2,$ a sphere of lead of density 'd' $\mathrm{kg}/{\mathrm{m}}^3$ is gently released in a column of liquid of density $\rho \mathrm{kg}/{\mathrm{m}}^3$. If $\mathrm{d}>\rho$, the sphere will

• (A) fall vertically with an acceleration 'g'
• (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

The Correct Option is C

Explanation:
Apparent weight $=$ actual weight - upthrust$$\begin{array}{rl}Vd{g}^{\prime }& =Vdg-V\rho g\\ \Rightarrow g^{\prime }& =\left(\frac{d-\rho }{d}\right)g\end{array}$$