A stone of relative density \(\mathrm{K}\) is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of

• A

  \(\mathrm{g}(1-\mathrm{K})\)
• B

  \(\mathrm{g}(1+\mathrm{K})\)
• Correct answer
  C

  \(\mathrm{g}\left(1-\frac{1}{\mathrm{~K}}\right)\)
• D

  \(\mathrm{g}\left(1+\frac{1}{\mathrm{~K}}\right)\)

Solution

Hints:
\(\begin{aligned} & F=v \sigma g-v \rho g=v \sigma g\left(1-\frac{\rho}{\sigma}\right)=m g\left(1-\frac{1}{\mathrm{k}}\right) \\ & a=g\left(1-\frac{1}{\mathrm{k}}\right) \end{aligned}\)

Hence, the correct answer is option: 'C'.