Prove that the SI unit of gravitatinal feild strength,N.kg to the power of minise 1,is equivalent tothe SI unit of acceleration due to gravity,m.s-2.
To prove that the SI unit of gravitational field strength, N.kg^(-1), is equivalent to the SI unit of acceleration due to gravity, m.s^(-2), we need to understand the definitions of both units and how they are related.
The unit N.kg^(-1) represents Newton per kilogram, which is the unit of force per unit mass. It describes the amount of force experienced by a mass at a specific location in a gravitational field.
The unit m.s^(-2) represents meters per second squared, which is the unit of acceleration. It describes the rate at which an object's velocity changes per unit time. In the context of gravity, it represents the rate at which an object's speed increases per second when falling freely near the Earth's surface.
Now, let's derive the equivalence between these two units:
1. Start with Newton's second law of motion: F = ma, where F is the force, m is the mass, and a is the acceleration.
2. In the case of the force of gravity near the Earth's surface, the force (F) acting on an object is given by the equation: F = mg, where g is the acceleration due to gravity.
3. Rearrange the equation to solve for g: g = F/m.
4. The force, F, is measured in Newtons (N), and mass, m, is measured in kilograms (kg). Therefore, g is given in N/kg, which is equivalent to N.kg^(-1).
5. Now, let's simplify the unit of N.kg^(-1) to m.s^(-2) to establish the equivalence. Recall that acceleration, a, is given by a = Δv/Δt, where Δv is the change in velocity, and Δt is the change in time.
6. Consider an object in free fall near the Earth's surface. As it falls, its velocity increases uniformly at a constant rate. The change in velocity, Δv, divided by the change in time, Δt, is the average acceleration of the object.
7. The average acceleration of an object in free fall near the Earth's surface is approximately 9.8 m/s^2. This value is defined as the standard average acceleration due to gravity, which is denoted by the symbol g, making g = 9.8 m/s^2, approximately.
From steps 4 and 7, we can conclude that the SI unit for gravitational field strength (N.kg^(-1)) is equivalent to the SI unit for acceleration due to gravity (m.s^(-2)).
Therefore, the proof is complete.