The instrument used for determining specific gravity is
$\left( {\text{A}} \right)$ Hydrometer
$\left( {\text{B}} \right)$ Barometer
$\left( {\text{C}} \right)$ Calorimeter
$\left( {\text{D}} \right)$ None of this

Hint:The concept of buoyancy of a substance is measured by the specific gravity and also which explains the tendency of the material to rise or sink when it is merged in the reference material.
Generally, we take water as the reference material. The measurement is based upon if the substance sinks or floats in the taken reference material.
The hydrometer is used in the concept of buoyancy of material to measure the relative density of a substance.

Complete step by step answer:
We have to find the instrument which is used for determining specific gravity from the given options.
First, we explain the definition of Specific Gravity. The specific gravity of a substance is measured by the ratio of the density of that substance to the density of reference material. Generally, we take water as the reference material. The measurement is based upon if the substance in the sink or float in the taken reference material.
The concept of buoyancy of a substance is measured by the specific gravity and also which explains the tendency of the material to rise or sink when it is merged in the reference material.
Now we go through the given options and find the right answer:
$\left( {\text{A}} \right)$ Hydrometer – This is the instrument that measures the relative density of a substance. As the Specific gravity is none then the ratio of the density of that substance to the density of reference material, it's also called the relative density of the substance.
The Hydrometer is used in the concept of buoyancy of the substance.
This is the right answer.

$\left( {\text{B}} \right)$ Barometer – This is the instrument that measures the air pressure for a certain environment.
This is not the right answer.

$\left( {\text{C}} \right)$ Calorimeter - This is the instrument that measures the heat of any chemical reactions or physical issues.

$\left( {\text{D}} \right)$ None of this – we get the answer from the given options.
So this is an invalid option.

Hence the correct option is $\left( {\text{A}} \right)$.

Notes:The Hydrometer is divided into two classes such as
\[\left( i \right)\] the weight of the substance is more than that of the water and
\[\left( {ii} \right)\] the weight of the substance is less than that of the water.