Question

An empty plastic box of mass m is found to acclerate 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 1

When the box accelerating upward,

$U-mg=\frac{mg}{6}$

$\Rightarrow U=\frac{7mg}{6}$

$\Rightarrow m=\frac{6U}{7g}$ ...(i)

$Mg-U=\frac{Mg}{6}$

$\Rightarrow Mg-\frac{Mg}{6}=U$

$\Rightarrow M=\frac{6u}{5}$ ....(ii)

Mass added = $\frac{6U}{5g}-\frac{6U}{7g}$

$=\frac{6U(7-5)g}{35g}$

$=\frac{6U.2g}{35g}$

From equation (i), m $=\frac{6U}{7g}$

$\therefore$ Added mass = $\frac{2}{5}mg$