A particle of mass m moves in the xy -plane with its position vector at time t given by r (t) = a ( t) i + b ( t) j , where a and b are positive constants such that a > b . Which of the following statements is correct regarding the dynamics of the particle?

Step-by-step solution

Given the position vector r (t) = a ( t) i + b ( t) j . Velocity of the particle: v (t) = d r dt = -a ( t) i + b ( t) j Acceleration of the particle: a (t) = d v dt = -a ^2 ( t) i - b ^2 ( t) j = - ^2 r (t) The force acting on the particle is F = m a = -m ^2 r . Since the force is always directed opposite to the position vector, it is a central force directed towards the origin. The torque about the origin is = r F = r (-m ^2 r ) = 0 . Since the net torque is zero, the angular momentum of the particle about the ori