if the units of mass,lenght and time are doubled, then the unit of force increases by _ %?

the answer is 0%, but please explain this answer using it's unit.. that is N = kg m s^-2

please give the answer with detailed explanation and solution. rates will be given for all answers.................

To understand how doubling the units of mass, length, and time affects the unit of force, we need to start with the fundamental definition of force itself. Force is defined by Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). The unit of force in the International System of Units (SI) is the Newton (N), which can be expressed in terms of its base units as follows:

Breaking Down the Units of Force

The unit of force is given by:

• 1 Newton (N) = 1 kg·m/s²

This means that a force of one Newton is the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

Understanding the Units

Now, let’s consider what happens when we double the units of mass, length, and time:

• If we double the mass, we have: m' = 2m
• If we double the length, we have: d' = 2d
• If we double the time, we have: t' = 2t

Acceleration and Its Impact

Acceleration is defined as the change in velocity over time, which can be expressed as:

• a = Δv/Δt

When we double the time, the acceleration will also change. If we consider a scenario where the velocity is constant, doubling the time will halve the acceleration because:

• a' = Δv/(2Δt) = (1/2)(Δv/Δt) = (1/2)a

Calculating the New Force

Now, substituting the new values into the force equation:

• F' = m'·a' = (2m)·(1/2)a = 2m·(1/2)a = ma

As you can see, the new force (F') is equal to the original force (F). Therefore, the force does not change when we double the units of mass, length, and time.

Percentage Change in Force

To find the percentage change in force, we can use the formula:

• Percentage Change = ((New Value - Original Value) / Original Value) × 100%

Since the new force is equal to the original force:

• Percentage Change = ((F - F) / F) × 100% = 0%

Final Thoughts

In summary, when the units of mass, length, and time are all doubled, the unit of force remains unchanged, resulting in a 0% increase in force. This illustrates the principle that while the individual units may change, the relationships defined by physics remain consistent, leading to no net change in the calculated force.