A rock has mass 1.80 kg. When the rock is suspended from the lower end of a string and totally immersed in water, the tension in the string is 10.8 N . What is the smallest density of a liquid in which the rock will float?

The density is  

Explanation:

From the question we are told that

    The mass of the rock is  

     The  tension on the string is  

Generally the weight of the rock is  

=>    

=>  

Now the upward force(buoyant force) acting on the rock  is mathematically evaluated as  

substituting values

This buoyant force is mathematically represented as

Here   is the density of water and it value is

 So

Now for this rock to flow the upward force (buoyant force) must be equal to the length

Here z is smallest density of a liquid in which the rock will float

=>    

=>  

=>