We know that Force = Mass * Accelaration; Hence, Accelaration = F/Mass

Case 1: Emply plastic box of mass M placed in water results in acceleration of g/6 upwards

Let V and ρ be the volume and density of the plastic box respectively

Hence, Force = Vρg – Mg as the acceleration acts upwards

Now F/mass = a; Hence, Vρg – Mg / M = g/6

Solving by cancelling g on both sides, we get 6 Vρ = 7 M  ------------Eqn (1)

Case 2 : Add sand to the empty plastic box so that it accelerates down

Let the mass of sand be m

(M + m)g – Vρg / M + m = g/6

Solving by cancelling g on both sides, we get 6 Vρ = 5 (M +m)  ------------Eqn (2)

From eqn (1) and eqn (2), we get 7M = 5M + 5m Hence, mass of sand = 2/5 M