A stone of relative density k is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of

If m is the mass of the stone and V its volume, the weight of the water displaced by it $=\rho Vg=$ ${\rho }^{\text{'}}\times \frac{m}{\rho }\times g=\frac{mg}{k}$, where ${\rho }^{\text{'}}$ is the density of water. Therefore, $k=\rho /{\rho }^{\text{'}}$. Thus, the buoyant force acting upwards is mg/k whereas the weight mg of the stone acts vertically downwards.

Therefore, the net force in the downward direction = $mg-\frac{mg}{k}$= $mg\left(1-\frac{1}{k}\right)$. If a is the acceleration of the sinking stone, then
$$\begin{gathered} ma=mg\left(1-\frac{1}{k}\right) \\ \text{ or } a=g\left(1-\frac{1}{k}\right) \end{gathered}$$
Hence the correct choice is (c).