Question

The gravitational potential at a place varies inversely with \( x^2 \) (i.e., \( V = kx^2 \)), the gravitational field at that place is

• A. \( \frac{2k}{x^3} \)
• B. \( \frac{-2k}{x^3} \)
• C. \( \frac{k}{x} \)
• D. \( \frac{-k}{x} \)

Hint:

Gravitational field is the negative derivative of the gravitational potential with respect to distance.

Answer 1

The Correct Option is B

Step 1: Relationship between potential and field.
Gravitational field is the negative gradient of the potential: \[ E = -\frac{dV}{dx} \] For \( V = kx^2 \), differentiating with respect to \( x \) gives the gravitational field as \( E = \frac{-2k}{x^3} \).

Step 2: Conclusion.
The gravitational field at that point is \( \frac{-2k}{x^3} \), which is the correct answer.