# Solve the following :

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 ?

Solution:

$\frac{m g}{6}=-(m g-B)$

$(m+\propto) \frac{g}{6}=(m+\propto) g-B$

B force is constant

$\frac{m g}{6}+m g=(\mathrm{m}+\propto) g-(\mathrm{m}+\propto) \frac{g}{6}$

$=>\frac{m g}{6}+m g=m g+\propto g-\frac{\mathrm{mg}}{6}-\frac{\propto g}{6}$

$\Rightarrow 2 \frac{m g}{6}=\frac{5 \propto g}{6}$

$\alpha=\frac{2 m}{5}$