A block of wood of mass 300 g and density 0.75 g/cm³ is floating on the surface of a liquid of density 1.1 g/cm³. What mass of lead density = 11.3 g/cm³) must be added to the block in order for the combination just to be submerged?

Question

Quizplus · Accepted Answer

First, we need to determine the volume of the wooden block. We use the formula:

Density = Mass / Volume

Rearranging this formula gives us:

Volume = Mass / Density

Substituting the given values, we get:

Volume of wooden block = 300 g / 0.75 g/cm^3 = 400 cm^3

Since the block is floating, it displaces a volume of liquid equal to its own volume. Therefore, the weight of the displaced liquid is:

Weight of displaced liquid = Volume of liquid displaced x Density of liquid

Substituting the given values, we get:

Weight of displaced liquid = 400 cm^3 x 1.1 g/cm^3 = 440 g

In order to submerge the block, we need to add enough lead so that the weight of the combination (wooden block + lead) is equal to the weight of the displaced liquid. Let the mass of lead added be x g. Then we have:

Weight of wooden block + Weight of lead = Weight of displaced liquid

300 g + x g = 440 g

Solving for x, we get:

x = 140 g

Therefore, we need to add 140 g of lead to the block in order to just submerge it. Thus, the best choice is D.

A Block of Wood of Mass 300 G and Density