Weight - Buoyancy = (mass x Gravity) - Buoyancy
Since the net acceleration is g/6 upwards, then we have:
a = -g/6;
we also know that a = F / m.
[Note this is a -ve sign because the acceleration is in the opposite direction to gravity]
so:
a = -g/6 = [(m x g) - B] / m
Solving for B:-
g/6 = mg/m - B/m
B/m = g + g/6
B = gm [1 + 1/6]
B = 7/6 x gm
After the sand is added in the new mass is (m + ms) and a = g/6.
Net Force = weight of box + weight of sand - Buoyancy
Net Force = m x g + ms x g - B
B = 7/6 x gm
So Net force = mg + ms x g - 7/6 x gm = ms x g - gm/6= g [ ms - m/6]
Force = mass x acceleration.
Now mass total is m + ms and acceleration is g/6
So g [ ms - m/6] = F = (m+ms)x a
g [ms - m/6] = (m + ms) x g/6ms - m/6 = (m + ms) 1/6ms - 1/6 ms = m/6 + m/65/6 ms = 2m/65 ms = 2mms = 2m/5
Hence, the mass = 2 x 5/5 = 2