Question

An empty plastic bottle of mass m is found to accelerate up at the rate of g/6 when placed deep inside water, what amount of sand must be put inside the bottle to accelerate it at the rate of g/6 downward?

Answer 1

Force of buoyancy  on the empty plastic bottle = m g + m * g/6

     Volume * 1000 kg/m³ * g =  7 m g / 6
     Volume = 7 m / 6000    m³

Let X kg of sand be put inside the empty bottle and bottle be sealed.

     buoyancy force (same as before) =  (m+X) * 5 g / 6
       ( 7 m / 6000 ) * 1000 * g  = (m+X) 5 g / 6

         7 m = 5 m + 5 X

           X = 2 m / 5

You need to fill with sand,  whose weight (mass) equal to 40% of the weight (mass) of empty bottle.