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 isCorrect answer : p²/rm How to solve?

Question

Answer

P=mv

Answer

Explanation:

To determine the radial force acting on a particle executing uniform circular motion, we can start by considering the definition of linear momentum and centripetal force.

Linear Momentum:
The linear momentum (p) of a particle is defined as the product of its mass (m) and its velocity (v).

p = m * v

Centripetal Force:
The centripetal force (Fc) is the force required to keep an object moving in a circular path. It always acts towards the center of the circle and is given by the equation:

Fc = m * (v^2 / r)

where m is the mass of the particle, v is its velocity, and r is the radius of the circular path.

Radial Force:
The radial force (Fr) is the force acting along the radial direction, i.e., along the radius of the circular path. It is the component of the centripetal force in the radial direction.

To find the radial force, we can resolve the centripetal force (Fc) into its radial and tangential components using trigonometry. The radial component of the force is equal to the centripetal force.

Fr = Fc

Resolving the Centripetal Force:
Using trigonometry, we can express the velocity (v) in terms of the angular velocity (ω) and the radius (r).

v = ω * r

Substituting this expression for v in the centripetal force equation, we get:

Fc = m * ((ω * r)^2 / r) = m * ω^2 * r

Final Expression for Radial Force:
Since the radial force (Fr) is equal to the centripetal force (Fc), we have:

Fr = Fc = m * ω^2 * r

Now, we know that the linear momentum (p) is given by:

p = m * v = m * (ω * r)

Squaring both sides of this equation, we get:

p^2 = (m * ω * r)^2

Comparing this with our expression for the radial force (Fr), we can conclude that:

Fr = p^2 / (m * r)

Therefore, the magnitude of the radial force acting on the particle is p²/rm.

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