Question

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?

• A. $2m/3$
• B. $2m/5$
• C. $m/5$
• D. $6m/7$

Answer 1

The correct option is B $2m/5$

For empty box
$F-mg=\frac{mg}{6}$
$F=\frac{7}{6}mg$
Let $m^{\prime }$ is the mass of sand filled inside the box.
$(m+m^{\prime })g-F=(m+m^{\prime })\frac{g}{6}$
$(m+m^{\prime })g-\frac{7}{6}mg=(m+m^{\prime })\frac{g}{6}$
$\frac{5}{6}{m}^{\prime }=\frac{1}{3}m$
$\Rightarrow m^{\prime }=\frac{2}{5}m$