Question

To get your gold down river you want to put it on a raft, but you're worried that the raft might sink. What equation correctly gives the maximum amount of gold that you can put on top of your raft? (All symbols have their usual meaning.)

1) Mgold = Vraft * g * (Praft - Pwater)

2) Mgold = Vraft * g * (Pwater- Praft)

3) Mgold = Vraft * (Praft - Pwater)

4) Mgold = Vraft * (Pwater- Praft)

Answer 1

Let,

Mass of raft = M

Mass of gold = m

Volume of raft = Vraft

Density of raft =

Density of water =

Buoyancy force = F

Now, we can put the gold on the raft till it just sink into the water as shown in the figure so, by balancing the forces:

Where, Buoyancy force on raft is :

Therefore,

Answer (4)