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: Relationship between centripetal force and linear momentum.
The centripetal force \( F_c \) for a particle in uniform circular motion is given by: \[ F_c = \frac{mv^2}{r}, \] where \( m \) is the mass of the particle, \( v \) is its velocity, and \( r \) is the radius of the circular path. The magnitude of linear momentum \( p \) is given by: \[ p = mv. \] Step 2: Ratio of \( F_c \) to \( p \).
The ratio of centripetal force to linear momentum is: \[ \frac{F_c}{p} = \frac{\frac{mv^2}{r}}{mv} = \frac{v}{r}. \] Step 3: Conclusion.
The ratio of centripetal force to linear momentum is \( v/r \). \[ \therefore \text{The correct answer is: \( v/r \).} \]