A particle of mass m is executing uniform circular motion on a path of radius r. If P is the magnitude of its linear momentum. The radial force acting on the particle is
Correct answer: C. P2/mr
- A. mP2/r
- B. rm/P
- C. P2/mr
- D. Pmr
Explanation
Option C is correct.The radial force is the centripetal force that keeps the particle moving in a circular path. The centripetal force is given by the following formula:Fc = mv2/r where:Fc is the centripetal force (N).m is the mass of the particle (kg).v is the speed of the particle (m/s).r is the radius of the circle (m).We can write the magnitude of the linear momentum as: P = mv. Substituting this into the equation for the centripetal force, we get: Fc =P2/mr. Therefore, the radial force acting on the particle is P2/mr.Options A, B, and D are incorrect because they do not appropriately consider the relationship between linear momentum and centripetal force in uniform circular motion.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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