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A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle.
The motion of the particle takes place in a plane. It follows that :
The motion of the particle takes place in a plane. It follows that :
- a)its velocity is constant
- b)its acceleration is constant
- c)its kinetic energy is constant.
- d)it moves in a circular path.
Correct answer is option 'C,D'. Can you explain this answer?
Verified Answer
A particle is acted upon by a force of constant magnitude which is alw...
When the force is perpendicular to the velocity and constant in magnitude then the force acts as a centripetal force, and the body moves in a circular path. The force is constant in magnitude, this show the speed is not changing and hence kinetic energy will remain constant.
Note : The velocity changes continuously due to change in the direction. The acceleration also changes continuously due to change in direction.
Most Upvoted Answer
A particle is acted upon by a force of constant magnitude which is alw...
Explanation:
When a particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, several characteristics of its motion can be observed.
Constant Velocity:
Since the force is always perpendicular to the velocity, it does not change the magnitude of the velocity. However, it does change the direction of the velocity. Therefore, the particle moves along a circular path with a constant speed, resulting in constant velocity.
Constant Acceleration:
Acceleration is defined as the rate of change of velocity. In this case, since the force is always perpendicular to the velocity, it does not cause any change in the magnitude of the velocity. Therefore, the acceleration of the particle is always directed towards the center of the circular path and its magnitude remains constant. This is known as centripetal acceleration.
Constant Kinetic Energy:
Kinetic energy is defined as the energy possessed by an object due to its motion. In this case, since the magnitude of the velocity remains constant, the kinetic energy of the particle also remains constant. The force acting on the particle does not do any work on it, as the force is always perpendicular to the displacement of the particle. Therefore, there is no change in the kinetic energy of the particle.
Motion in a Circular Path:
Since the force acting on the particle is always perpendicular to the velocity, it continuously changes the direction of the particle's motion. This results in the particle moving in a circular path. The force acting as the center-seeking force is responsible for keeping the particle in its circular path.
Therefore, the correct options are C (its kinetic energy is constant) and D (it moves in a circular path). The particle's velocity is constant due to the perpendicular force, and its acceleration is also constant and directed towards the center of the circular path.
When a particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, several characteristics of its motion can be observed.
Constant Velocity:
Since the force is always perpendicular to the velocity, it does not change the magnitude of the velocity. However, it does change the direction of the velocity. Therefore, the particle moves along a circular path with a constant speed, resulting in constant velocity.
Constant Acceleration:
Acceleration is defined as the rate of change of velocity. In this case, since the force is always perpendicular to the velocity, it does not cause any change in the magnitude of the velocity. Therefore, the acceleration of the particle is always directed towards the center of the circular path and its magnitude remains constant. This is known as centripetal acceleration.
Constant Kinetic Energy:
Kinetic energy is defined as the energy possessed by an object due to its motion. In this case, since the magnitude of the velocity remains constant, the kinetic energy of the particle also remains constant. The force acting on the particle does not do any work on it, as the force is always perpendicular to the displacement of the particle. Therefore, there is no change in the kinetic energy of the particle.
Motion in a Circular Path:
Since the force acting on the particle is always perpendicular to the velocity, it continuously changes the direction of the particle's motion. This results in the particle moving in a circular path. The force acting as the center-seeking force is responsible for keeping the particle in its circular path.
Therefore, the correct options are C (its kinetic energy is constant) and D (it moves in a circular path). The particle's velocity is constant due to the perpendicular force, and its acceleration is also constant and directed towards the center of the circular path.
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