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 accerelate down at the rate of g/6?

Answer 1

Let buoyant force be F.

Now F - m g = m g/6

Which gives F = 7mg/6

Let M be the mass of sand to be put to give acceleration g/6 down. Writing equation of motion, (m+M) g - F = (m+M)g/6

Putting value of F we get,

(m +M)g - 7mg/6 = (m+M) g/6

mg +Mg -7mg/6 =mg/6 + Mg/6

Mg(1–1/6) = mg (1/6+7/6–1)

Mg × 5/6 = mg ×2/6

M = 2mg/5

......hope it helps u....

Answer 2

Answer:

7m

Explanation:

Mass of sand required =2m/5

Let the Volume of the plastic box be V

In the first case, when the box is accelerating upwards at g/6 :

Vρg−mgm=g/6

Therefore, 6Vρ=7m

In the second case, let M mass of sand has been put inside the box :

(m+M)g−Vρg(m+M)=g6

Therefore, 5(m+M)=6Vρ

comparing the equations from the two cases :

5(m+M)=7m

or, M=2m5