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
Lets do this the long way.
In the water, the net force=mass*acceleration (neglecting considerable friction).
but net force=bouyantforce-mg 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 mg-mg-Mg=-1/4 mg
solve for M
check all this.posted by bobpursley