A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of particle. The motion of particle takes place in a plane it follows that : A its velocity is constant option B its kinetic energy is constant C its acceleration is constant. D it moves in a straight line Answer: B ; Why not A? Please explain.?

Question

Answer

F=mrw^2F=mv^2/rNow F IS CONSTANTThus,mv^2/r is constantNow r will be constant Thus mv^2 is constantThis implies Kinetic energy I.e. mv^2/2 is also constantHere velocity and acceleration will not be constant since velocity is a vector quantity and in a circular motion velocity will keep changing.

Answer

Answer

The motion of a particle under the influence of a constant perpendicular force

Introduction:
When a particle is acted upon by a force of constant magnitude that is always perpendicular to its velocity, the motion of the particle takes place in a plane. In such a scenario, it is important to analyze the behavior of the particle in terms of its velocity, kinetic energy, acceleration, and the path it follows.

Velocity:
In this situation, the velocity of the particle is not constant. Since the force is always perpendicular to the velocity, it only changes the direction of the velocity vector but not its magnitude. Consequently, the particle moves along a circular path, constantly changing its direction. Therefore, option A stating that the velocity is constant is incorrect.

Kinetic Energy:
The kinetic energy of a particle is given by the equation KE = 1/2 mv^2, where m is the mass of the particle and v is its velocity. As discussed earlier, the magnitude of the velocity remains constant throughout the motion. Since the kinetic energy depends only on the magnitude of the velocity, it remains constant in this case. Hence, option B stating that the kinetic energy is constant is correct.

Acceleration:
The acceleration of a particle is defined as the rate of change of its velocity with respect to time. In this scenario, the force acting on the particle is always perpendicular to its velocity. As a result, the force does not contribute to any change in the magnitude of the velocity. Thus, the magnitude of the velocity remains constant, leading to zero acceleration. Therefore, option C stating that the acceleration is constant is incorrect.

Motion:
Since the particle experiences a constant perpendicular force, it moves in a circular path. The force acting as a centripetal force keeps the particle moving in a curved trajectory. Therefore, option D stating that it moves in a straight line is incorrect.

Conclusion:
In summary, when a particle is acted upon by a force of constant magnitude that is always perpendicular to its velocity, the velocity is not constant but its kinetic energy remains constant. The acceleration is zero, and the particle moves in a circular path rather than a straight line. Thus, option B stating that the kinetic energy is constant is the correct answer to the given scenario.

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