According to classical mechanics, the magnitude of centrifugal force on a body moving in a circular path increases with which of the following (assuming mass and radius of the path remain constant)?

Introduction / Context:
When a body moves in a circular path, it experiences a centripetal acceleration towards the centre of the circle. In a rotating reference frame, an apparent outward force called centrifugal force is considered. The magnitude of this force depends on the motion parameters. This question checks whether you understand which type of physical quantity influences the size of centrifugal force when mass and radius are fixed.

Given Data / Assumptions:

• A body of constant mass moves in a circular path of fixed radius.
• We are interested in how centrifugal force changes with other physical quantities.
• Options include temperature, pressure, acceleration and humidity.
• We consider uniform circular motion under classical mechanics.

Concept / Approach:
In uniform circular motion, the centripetal acceleration a_c needed to keep an object moving in a circle of radius r with linear speed v is given by a_c = v^2 / r. The corresponding centripetal force is F_c = m * a_c = m * v^2 / r. In a rotating frame, the outward centrifugal force has the same magnitude. If the angular speed or linear speed increases while mass and radius remain constant, the centripetal acceleration and therefore the force increase. Thus, centrifugal force increases with the magnitude of the centripetal acceleration. Temperature, pressure and humidity are thermodynamic or environmental properties and do not directly enter the expression for centrifugal force in this simple mechanical model.

Step-by-Step Solution:
Step 1: Write the formula for centripetal acceleration in circular motion: a_c = v^2 / r, where v is linear speed and r is radius. Step 2: Express the corresponding centripetal force as F_c = m * a_c = m * v^2 / r. Step 3: Recognise that in a rotating reference frame, centrifugal force has the same magnitude as centripetal force but acts outward. Step 4: For fixed mass m and radius r, the only variable that affects F_c is v or equivalently a_c. Step 5: As speed v increases, the centripetal acceleration a_c increases, and therefore the centrifugal force also increases. Step 6: Acceleration is the quantity in the options that directly relates to this effect, since F is proportional to acceleration. Step 7: Temperature, pressure and humidity may affect fluid properties in some advanced cases, but they are not part of the basic expression for centrifugal force.

Verification / Alternative check:
Consider a stone tied to a string and whirled in a circle. When you increase the speed of rotation, you feel a stronger pull on your hand, indicating an increase in the force associated with circular motion. That increased pull corresponds to a larger centripetal acceleration and therefore a larger centrifugal force in the rotating frame. No change in temperature, pressure or humidity is needed to observe this effect; it depends purely on the acceleration associated with circular motion. This simple demonstration confirms that centrifugal force increases with acceleration.

Why Other Options Are Wrong:
Temperature is a measure of thermal energy and does not appear in the basic formula for centripetal or centrifugal force. Pressure is force per unit area in fluids and is unrelated to the mechanical expression F = m * v^2 / r for circular motion. Humidity describes moisture content in air and does not directly influence centrifugal force in the classical mechanics formula.

Common Pitfalls:
In more complex systems involving rotating fluids or atmospheric phenomena, temperature and pressure can affect density and flow patterns, which may change forces indirectly. However, at the level of basic physics tested in such questions, you should focus on the direct mathematical relationship. Remember that centrifugal force magnitude is directly proportional to centripetal acceleration and depends on mass, radius and speed, not on thermal or environmental variables. This helps you choose acceleration as the correct answer quickly.

Final Answer:
For a body moving in a circular path with fixed mass and radius, centrifugal force increases with acceleration associated with the circular motion.