What does the formula \( W = mg \) signify in physics?

What does the formula \( W = mg \) signify in physics?

• A. Work done is the product of mass and acceleration
• B. Weight is equal to mass times the acceleration due to gravity
• C. Energy is the product of work and time
• D. Power is the rate of work compared to gravity

Answer: (B)

The formula \( W = mg \) signifies that weight is equal to mass multiplied by the acceleration due to gravity. In this context, \( W \) represents the weight of an object, \( m \) represents its mass, and \( g \) is the acceleration due to gravity, which typically has a value of approximately \( 9.81 \, \text{m/s}^2 \) on the surface of the Earth. This relationship is fundamental in mechanics because it directly relates the gravitational force acting on an object to its mass. Weight is a specific force that acts downwards due to gravity, and it is proportional to the object's mass. This means that as the mass of an object increases, its weight also increases correspondingly when subjected to the same gravitational field. In practical applications, this formula helps in calculating the force required to lift an object in a gravitational field. Understanding this concept is critical for analyzing various physical systems where gravitational forces play a significant role, such as in free-fall motion or when determining the forces acting on structures. Other options do not accurately reflect this relationship. The formula specifically emphasizes the connection between weight and gravitational acceleration, rather than work or power dynamics with respect to time.

The formula ( W = mg ) signifies that weight is equal to mass multiplied by the acceleration due to gravity. In this context, ( W ) represents the weight of an object, ( m ) represents its mass, and ( g ) is the acceleration due to gravity, which typically has a value of approximately ( 9.81 , \text{m/s}^2 ) on the surface of the Earth.

This relationship is fundamental in mechanics because it directly relates the gravitational force acting on an object to its mass. Weight is a specific force that acts downwards due to gravity, and it is proportional to the object's mass. This means that as the mass of an object increases, its weight also increases correspondingly when subjected to the same gravitational field.

In practical applications, this formula helps in calculating the force required to lift an object in a gravitational field. Understanding this concept is critical for analyzing various physical systems where gravitational forces play a significant role, such as in free-fall motion or when determining the forces acting on structures.

Other options do not accurately reflect this relationship. The formula specifically emphasizes the connection between weight and gravitational acceleration, rather than work or power dynamics with respect to time.