For a varying force work done can be expressed as aa)product of force and displacementb)force divided by the displacementc)definite integral of force over displacementd)differentiation of force with displacementCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

For a variable force, the work done can be expressed as a definite integral of force over displacement for any system.In case of a variable force, the is calculated with the help of integration. For example, in the case of a spring, the force acting upon any object attached to a horizontal spring can be given as Fs = -kx, where k is the spring constant and x is the displacement of the object attached. We can see that this force is proportional to the displacement of the object from the equilibrium position, hence the force acting at each instant during the compression and extension of the spring will be different. Thus, the infinitesimally small contributions of work done during each instant are to be counted in order to calculate the total work done.

Answer

Explanation:

Definite Integral of Force over Displacement:
- When a force is varying, the work done can be calculated by finding the definite integral of the force over displacement.
- This involves finding the area under the force vs. displacement graph, which represents the work done.
- By integrating the force function with respect to displacement, the work done can be accurately determined.

Product of Force and Displacement:
- While the product of force and displacement gives the work done for a constant force, it may not accurately represent the work done for a varying force.
- For varying forces, the relationship between force and displacement may not be linear, making the product of force and displacement an inaccurate measure of work done.

Force Divided by Displacement:
- Dividing force by displacement does not provide a meaningful measure of work done, as work is the product of force and displacement, not their ratio.
- This calculation does not take into account the varying nature of the force and its effect on the work done.

Differentiation of Force with Displacement:
- Differentiating force with displacement gives the rate of change of force with respect to displacement, which is not directly related to the work done.
- While differentiation is useful for understanding how force changes with displacement, it does not give a direct measure of the work done.

In conclusion, the most accurate way to calculate work done for a varying force is to find the definite integral of the force function over displacement. This method takes into account the varying nature of the force and provides a precise measure of the work done.

Answer

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