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Question: The potential energy of a body is given by \(A - B x ^ { 2 }\) (where x is the displacement). The ...

The potential energy of a body is given by A−Bx2A - B x ^ { 2 } (where x is the displacement). The magnitude of force acting on the particle is

A

Constant

B

Proportional to x

C

Proportional to x2x ^ { 2 }

D

Inversely proportional to x

Answer

Proportional to x

Explanation

Solution

F=−dUdx=−ddx(A−Bx2)=2BxF = \frac { - d U } { d x } = - \frac { d } { d x } \left( A - B x ^ { 2 } \right) = 2 B x ∴ F ∝ x .