Question

a empty plastic box in water having acceleration of g/6 upward.how much sand is required that the box will move with acceleration of g/6 downward?

Answer 1

The mass of the empty plastic box is $m$ and its acceleration $a = g/6$ is upward. If sand of mass $M$ is put into box the mass becomes $m + M$ and acceleration becomes $a = -g/6$. Let $B$ be the force of buoyancy. Then

$$\left\{ \begin{array}{c} -mg + B = \frac{mg}{6} \\ -(m + M)g + B = -\frac{(m + M)g}{6} \end{array} \right. \gg -Mg + \frac{mg}{6} = -\frac{(m + M)g}{6} \gg M = \frac{2}{5}m$$