An empty plastic box of mass m is found to accelerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?

Explanation

Let the air resistance force is `F_a` aned Bouyant force is B.
Given that, `F_a =av`
where v= velocity
`rarr F_M=kv, `
where k= proportioN/Ality constant

When the ballon is moving downward
`B+kv=Mg` ................i.
`rarr m= (b+kv)/g`
`for the balloon to rise with a constant velocity v (upward) let the mass of m
` Here , B-(mg+kv)=0`
` B=mg+kv` ltbr. `rarr m=(B+kv)/g`
`:.` Amount of mass that should be removed =M-m`
`=(B+kv)/g- (B-kv)/g`
` = (B+kv-B+kv)/g`
`(2kv)/g= (2(Mg-B))/g`
`2{M-B/g}`