Question

The potential energy for a force field is given by U(x,y) = (x+y). The force acting on a particle at position given by coordinates (0, π/4) is:

• A. 1√(2)(i + j)
• B. -1√(2)(i + j)
• C. (12i + √(3)2j)
• D. (12i - √(3)2j)

Hint:

Force in a conservative field is always the negative gradient of potential energy.

Answer 1

The Correct Option is A

Step 1: Force is given by negative gradient of potential: F = - U
Step 2: ( U)/( x) = -(x+y), ( U)/( y) = -(x+y)
Step 3: F = (x+y)(i + j)
Step 4: At (0, π/4), (π/4) = 1√(2)