Question

A uniform diameter rod is weighted at end and is floating in a liquid. Determine if the liquid is (a) lighter than water, (b) water, or (c) heavier than water. Justify your answer.

Answer 1

(C) Heavier than water

Explanation:

Given

Diameter of the rod is uniform

The road is floating in a liquid.

Let the area of cross-section of the rod = A

Let the weight density of water = γw

Let the weight density of liquid = γl

Let the density of water = ρw

g is the gravitational force

So, weight of rod = density of the rod X volume

Wrod = ρw X g X ( A X 2L) + 2 ρwg (A X L)

Wrod = 4ρwgAL

Wrod = 4γwAL

We can see that the weight of the rod is more than the density of water. So, in water, the rod will sink.

If the rod is floating on the liquid then the liquid is heavier than the water.

Therefore, The liquid is heavier than the water.