If x,v and a denote the displacement, the velocity and the acceleration of a particle
executing simple harmonic motion of time period T, then which of the following do not
change with time?
Correct option is A. $$\dfrac{aT}{v}$$
$$\because$$ In option $$(a),\dfrac{aT}{v}=\dfrac{\dfrac{m}{s^2}\times s}{\left(\dfrac{m}{s}\right)}=\dfrac{m\times s^2}{m\times s^2}=[M^0L^0T^0]$$
So, according to the result above relation does not depend on time