Question

A particle of mass \(m\) moves in a central force field \(F(r)\). Which physical quantity remains conserved during this motion?

• A. Linear momentum
• B. Angular momentum
• C. Kinetic energy
• D. Velocity

Hint:

For any {central force}, torque about the center is zero, so {angular momentum is conserved}.

Answer 1

The Correct Option is B

Concept: A central force is a force that is always directed along the line joining the particle and a fixed point (the center) and whose magnitude depends only on the distance \(r\). Examples include gravitational force and electrostatic force.
Step 1: Understand torque in a central force.} Torque is given by \[ \vec{\tau} = \vec{r} \times \vec{F} \] In a central force field, the force \(\vec{F}\) acts along the direction of \(\vec{r}\). Thus, \[ \vec{\tau} = \vec{r} \times \vec{F} = 0 \]
Step 2: Apply angular momentum relation.} Since \[ \vec{\tau} = \frac{d\vec{L}}{dt} \] and \(\vec{\tau} = 0\), \[ \frac{d\vec{L}}{dt} = 0 \] Therefore, \[ \vec{L} = \text{constant} \] Thus, angular momentum remains conserved.