Rankers Physics

Potential Energy & Equilibrium: Practice Problem & Solution

In a conservative field, the potential energy U as a function of position x is given by U = x². Then the corresponding conservative force is given by
x
2x
-x
-2x

Solution Explained:

To solve this problem, we apply the core principles of Potential Energy & Equilibrium. Understanding the underlying formula is key to arriving at the correct answer below:

By definition Force F = -dU/dx, so 

F = - d(x²)/dx= -2x

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A uniform chain has a mass m and length l. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is
2. When a spring is stretched by 1 cm, it stores energy 50 J. If it is further stretched by 1 cm, the stored energy will be
3. The potential energy of a long spring when stretched by \(2\text{ cm}\) is \(U\). If the spring is stretched by \(8\text{ cm}\) the potential energy stored in it is: (2006)
4. Assertion (A): When a non-conservative force is involved in a system, it may dissipate energy. Reason (R): The work done by a non-conservative force is always negative.
5. Given below are two statements: Assertion (A): A block of mass \(m\) is dropped from a height \(h\) on to a spring of spring constant \(k\). The maximum compression \(x_{\text{max}}\) in the spring is given by \(x_{\text{max}} = \sqrt{\frac{2mgh}{k}}\) Reason (R): The work done by gravitational force is equal to the elastic potential energy stored in the spring at maximum compression. In the light of the above statements, choose the correct answer from the options given below.