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?

Options

A. `(2m)/(3)`
B. `(2m)/(5)`
C. `(3m)/(4)`
D. `(3m)/(5)`

Answer

B

Explanation

`F_(0)-mg=ma=(mg)/(6)`
`F_(0)=(7mg)/(6)`

`m_(0):` mass of sand
`(m+m_(0))g-F_(0)=(m+m_(0))=(m+m_(0))(g)/(6)`
`5(m+m_(0))(g)/(6)=F_(0)=(7mg)/(6)`
`5m+5m_(0)=7mrArrm_(0)=(2m)/(5)`