(a) The elastic limit is the maximum stress that a material can withstand without undergoing permanent deformation. It is the point beyond which the material will deform plastically.

(b) To calculate Young's modulus (Y), we use the formula: Y = Force / Extension. We can choose any point on the straight, elastic portion of the graph. Let's choose a point where the force is 50N and the extension is 0.02m (2cm). Therefore, Y = 50N / 0.02m = 2500 N/m² = 2500 Pa = 2.5 x 10³ Pa = 2.5 x 10³ GPa. (The exact value will depend on the chosen point on the graph).

(c) The elastic limit is important in engineering design because it ensures that the material will not undergo permanent deformation under normal operating conditions. If a component is subjected to a load exceeding the elastic limit, it will deform permanently, potentially leading to failure. Engineers must design components so that the applied stress remains below the elastic limit to prevent this from happening. This ensures the structural integrity and functionality of the design.

Experimental Procedure:

1. Materials: A small, lightweight object (e.g., a small piece of cardboard or foam), a controlled drop height (e.g., 1 metre), a measuring device (e.g., a stopwatch), a ruler or calipers to measure surface area, and a stand to ensure consistent drop conditions.
2. Procedure: Cut out multiple objects of the same shape but with varying surface areas (e.g., one with a large surface area, one with a medium surface area, and one with a small surface area). Drop each object from the fixed height, ensuring the drop is performed repeatedly (e.g., 5-10 times) for each surface area. Measure the time taken for each object to fall from the height.
3. Variables:

   • Independent Variable: Surface area of the object.
   • Dependent Variable: Time taken for the object to fall.
   • Controlled Variables: Drop height, initial velocity (ensure the object is released from rest), air conditions (e.g., conduct the experiment in a room with minimal drafts).

Analysis and Support for Friction (Drag):

The results of the experiment would show that objects with larger surface areas take longer to fall than objects with smaller surface areas. This is because the objects with larger surface areas experience a greater force of air resistance (drag). The drag force is proportional to the surface area of the object. The larger the surface area, the more air the object collides with, and the greater the opposing force. By controlling other variables, we can isolate the effect of surface area on air resistance, thus supporting the concept that friction (drag) is a force that opposes the motion of an object through a fluid (in this case, air). A graph of time vs. surface area would demonstrate this relationship.

If the force acting on an object moving in a circular path is increased while the mass and speed remain constant, the radius of the circular path will decrease. The centripetal force is required to constantly change the direction of the object's velocity, keeping it moving in a circle. The centripetal force is given by F = mv²/r, where 'F' is the centripetal force, 'm' is the mass, 'v' is the speed, and 'r' is the radius. Since the speed and mass are constant, the centripetal force is directly proportional to the radius. Therefore, an increase in the centripetal force will result in a smaller radius of the circular path. The object will move in a tighter circle.