Posted by usha on .
An empty plastic box of mass 9 kg is found to accelerate up at the rate of g/3 m/sec2 when placed deep inside water. Mass of the sand that should be put inside the box so that it may accelerate down at the rate of g/4 m/sec2 is

physics 
bobpursley,
Lets do this the long way.
In the water, the net force=mass*acceleration (neglecting considerable friction).
but net force=bouyantforcemg or
bouyant force=mass*g* 1/3 +mg=4/3 mg
this bouyant force does not change. So to go now,
bouyant force(m+Masssand)g=1/4 (M+m)
4/3 mgmgMg=1/4 mg
Mg=mg(.25+1.33)
solve for M
check all this.