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?
Answer & explanation
Correct answer: option 3
The upward acceleration is due to force of buoyancy applied by water on the plastic box. Let force of buoyancy is F.
Now F - mg = m $\frac{g}{6}$
⇒ F = $\frac{7mg}{6}$
Let M be the mass of sand to be put to give acceleration g/6 down. Then from equation of motion,
(m+M)g - $\frac{7mg}{6} = \frac{(m+M)g}{6}$
mg +Mg - 7mg/6 = mg/6 + Mg/6
Mg×5/6=mg2/6
M = $\frac{2m}{5}$