In the definition of weight, w = mg, the mass m refers to an inertial mass. T/F
The Correct Answer and Explanation is :
True.
In the equation ( w = mg ), where ( w ) represents weight, ( m ) denotes mass, and ( g ) is the acceleration due to gravity, the mass ( m ) specifically refers to inertial mass. Understanding the distinction between inertial mass and gravitational mass is essential in physics.
Inertial Mass is a measure of an object’s resistance to acceleration when a force is applied. It quantifies how much an object will accelerate in response to a given force, according to Newton’s second law, ( F = ma ). Here, ( a ) is the acceleration produced by the net force ( F ), and the inertial mass ( m ) is a proportionality constant. Thus, larger inertial mass means that more force is needed to achieve the same acceleration.
Gravitational Mass, on the other hand, is a measure of the strength of an object’s interaction with a gravitational field. It determines the force of gravity acting on the object, which is given by Newton’s law of universal gravitation: ( F = G \frac{m_1 m_2}{r^2} ), where ( G ) is the gravitational constant, ( m_1 ) is the mass of one object, ( m_2 ) is the mass of another object, and ( r ) is the distance between their centers.
The equivalence principle, proposed by Einstein, asserts that inertial mass and gravitational mass are equal. This means that the inertial mass that resists changes in motion is the same mass that responds to gravitational forces. As a result, when we calculate weight using ( w = mg ), we can use the inertial mass ( m ) in this context, since both masses behave identically under the influence of gravity.
In summary, the mass ( m ) in the weight equation ( w = mg ) is indeed inertial mass, reflecting its role in both acceleration and gravitational interaction, illustrating a fundamental principle of classical mechanics.