Inertial mass and Gravitational mass

Inertial mass

According to Newton's second law of motion (F = ma), the mass of a body can be determined by measuring the acceleration produced in it  by a constant force. (i.e) m = F/a. Intertial mass of a body is a measure of the ability of a body to oppose the production of acceleration in it by an external force.

If a constant force acts on two masses m_A and m_B and produces accelerations a_A and a_B respectively, then, F = m_Aa_A = m_Ba_B

m_A/ m_{B  =} a_{A /}a_B

The ratio of two masses is independent of the constant force. If the same force is applied on two different bodies, the inertial mass of the body is more in which the acceleration produced is less.

If one of the two masses is a standard kilogram, the unknown mass can be determined by comparing their accelerations.

Gravitational mass

According to Newton's law of gravitation, the gravitational force on a body is proportional to its mass. We can measure the mass of a body by measuring the gravitational force exerted on it by a massive body like Earth. Gravitational mass is the mass of a body which determines the magnitude of gravitational pull between the body and the Earth. This is determined with the help of a beam balance.

If F_A and F_B are the gravitational forces of attraction on the two bodies of masses m_A and m_B due to the Earth, then

F_A = Gm_AM /R²

F_B = Gm_BM /R²

where M is mass of the Earth, R is the radius of the Earth and G is the gravitational constant.

m_A/ m_{B  =} F_{A /}F_B

If one of the two masses is a standard kilogram, the unknown mass can be determined by comparing the gravitational forces.