Question

If \( p \) is the magnitude of linear momentum of a particle executing a uniform circular motion, then the ratio of centripetal force acting on the particle to its linear momentum is given by:

• A. \(v/r\).
• B. \(r/v\).
• C. \(v^2/r\).
• D. \(r/v^2\).

Hint:

In uniform circular motion, the centripetal force is proportional to \( v^2/r \), while the ratio to linear momentum simplifies to \( v/r \).

Answer 1

The Correct Option is A

Step 1: Define centripetal force and linear momentum.
Centripetal force \( F_c \) for uniform circular motion is calculated as:\[F_c = \frac{mv^2}{r},\]where \( m \) is mass, \( v \) is velocity, and \( r \) is the radius of the circular path.Linear momentum \( p \) is defined as:\[p = mv.\]Step 2: Calculate the ratio of \( F_c \) to \( p \).
The ratio \( F_c / p \) is derived as:\[\frac{F_c}{p} = \frac{\frac{mv^2}{r}}{mv} = \frac{v}{r}.\]Step 3: State the conclusion.
The ratio of centripetal force to linear momentum is determined to be \( v/r \).\[\therefore \text{The correct answer is: \( v/r \).}\]