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# Inertial mass and Gravitational 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.

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 mA and mB and produces accelerations aA and aB respectively, then, F = mAaA = mBaB

mA/ mB  = aA /aB

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 FA and FB are the gravitational forces of attraction on the two bodies of masses mA and mB due to the Earth, then

FA = GmAM /R2

FB = GmBM /R2

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

mA/ mB  = FA /FB

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

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Inertial mass and Gravitational mass |