Question

Two wooden boxes of equal mass but different density are held beneath the surface of a large container of water. Box A has a smaller average density than box B. When the boxes are released, they accelerate upward to the surface. Which box has the greater acceleration?

Answer 1

Step-by-step explanation:

Let boxes A and B has equal mass of M and volume be Va and Vb

their density be da and db

given da < db

M / Va < M/Vb

Va> Vb

Buoyant force on box A in water = weight of displaced water

= volume of displaced water x density of water x g

= Va x d x g , d is density of water

Aa = acceleration on box A

= buoyant force on A / mass of A

= Va x d x g / M

Similarly acceleration on box B

Ab = Va x d x g / M

Since Va > Vb

Aa > Ab

So box A will have greater acceleration.

Answer 2

Box A

Step-by-step explanation:

Let mass of each wooden box =m

Density of box A=
`\rho_A`

Density of box B =
`\rho_B`

`\rho_A<\rho_B`

Density,
`\rho=(m)/(V)`

`V_A=(m)/(\rho_A)`

`V_B=(m)/(\rho_B)`

Density of inversely proportional to volume.

The volume of box with smaller density is larger than the volume of box with large density.

`V_A>V_B`

When the boxes are submerged under water.

Then, the buoyant force=
`\rho_l Vg`

Where V=Volume of displace fluid.

`\rho=`Density of fluid

Buoyant force of box A=
`\rho_lV_Ag`

Buoyant force of box B=
`\rho_lV_Bg`

Force=Buoyant force

`ma_A=\rho_lV_Ag`

`ma_B=\rho_lV_Bg`

Acceleration is directly proportional to volume.

Therefore,the box with large volume has greater acceleration.

Hence, the box A has greater acceleration.