Constant of area velocity for a central force motion of a particle does not imply that_________
a)Equal areas were are swept by the radius vector in equal times.
b)The tangential velocity varies inversely as the length of the radius vectors
c)The angular momentus is conserved
d)The particle should stay in an orbit
To determine which option is incorrect, we need to understand the concept of the constant of area velocity in central force motion.
The constant of area velocity, also known as the conservation of angular momentum, is a principle in physics that states that when a particle moves under the influence of a central force, the rate at which it sweeps out equal areas in equal times remains constant. This means that as the particle moves along its path, the area it sweeps out in a fixed amount of time (for example, one second) will always be the same, regardless of its position.
Now let's analyze the options:
a) Equal areas are swept by the radius vector in equal times: This statement describes the constant of area velocity, which is true. When a particle moves under a central force, it indeed sweeps out equal areas in equal times, ensuring the conservation of angular momentum. Therefore, option a) is correct.
b) The tangential velocity varies inversely as the length of the radius vectors: This is also true. According to Kepler's second law, which is a result of the conservation of angular momentum, the tangential velocity of a particle in central force motion is proportional to the inverse of the length of the radius vectors. Hence, option b) is correct.
c) The angular momentum is conserved: This is true. The constant of area velocity implies the conservation of angular momentum. As long as no external torques act on the particle, its angular momentum remains constant. Therefore, option c) is correct.
d) The particle should stay in an orbit: This is the incorrect statement. The constant of area velocity does not imply that the particle should stay in an orbit. While a particle moving under central force motion can stay in an orbit, it is not a necessity. Depending on the initial conditions, the particle's trajectory could also be a straight line or a hyperbolic or parabolic path. Thus, option d) is the correct answer to the question.
In summary, the correct answer is d) The particle should stay in an orbit.