Question

If a body has a potential energy of \( (4x^2 + 2x) \, \text{J} \) at height 2 m, then the force acting on it is:

• A. \( 9 \, \text{N} \)
• B. \( 27 \, \text{N} \)
• C. \( 18 \, \text{N} \)
• D. \( 0 \, \text{N} \)

Hint:

Always use \( F = -\frac{dU}{dx} \) to find force from potential energy in mechanics.

Answer 1

The Correct Option is C

Force is negative gradient of potential energy: \( F = - \frac{dU}{dx} \)
Given \( U = 4x^2 + 2x \), then \[ F = -\left( \frac{d}{dx}(4x^2 + 2x) \right) = - (8x + 2) \]
At \( x = 2 \): \( F = - (8 \cdot 2 + 2) = -18 \, \text{N} \)
Magnitude = \( 18 \, \text{N} \)