Heating Mercury Affecting Floating Lead

[JSGandora]

Homework Statement

A flat, uniform cylinder of lead floats in mercury at 0 degrees Celsius. Will the lead float higher or lower then the mercury temperature is raised?

Homework Equations

None.

The Attempt at a Solution

Since the mercury is heated, then the density will be lower therefore the lead will float lower? I'm kind of confused because wouldn't it just sink to the bottom? Not remain floating?

 

[hale2bopp]

You could balance the forces acting on the body.
One will be mg, weight, acting downwards.
Other will be buoyant force, acting upwards. When they are equal, the body remains stationary in the liquid.
Now if you heat the mercury, the density of the mercury decreases, as you said, as its volume increases but mass remains constant.
Use the condition for the net force in the body to be zero, and apply the fact that the density has increased to get your answer.