Question

In a conservative field, the potential energy U as a function of position x is given as U=x²+x+3, then the corresponding conservative force is given by

(a) 2x+1
(b)−2x+1
(c) 2x+3
(d)−2x−1

Answer 1

The corresponding conservative force for a potential energy function U(x) = x² + x + 3 is found by taking the negative derivative of the potential energy with respect to x, resulting in -2x - 1, which corresponds to answer choice (d).

Step-by-step explanation:

The question is related to the relationship between conservative force and potential energy in physics. Given the potential energy function U(x) = x² + x + 3, we want to find the corresponding conservative force.

In physics, the formula for the force corresponding to the potential energy in a one-dimensional motion along the x-axis is given by F = -dU/dx, where U is the potential energy as a function of position and dU/dx is its derivative with respect to x.

Thus, the corresponding force F is:

1. Take the derivative of U with respect to x: dU/dx = 2x + 1.
2. Apply the negative sign as per the definition of conservative force: F = -(2x + 1).

Therefore, the answer is (d) −2x − 1.