when a ball allow to fall in four different path, 1 ) diagonal 2) parabolic 3)circular 4)vertical and then horizontal. The starting and final point are same, in which path it will take least time and why?
OCW Scholar - Physics I: Classical Mechanics
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To me, your question doesn't appear to be very clear. What do you exactly mean by 'circular' fall? The ball cannot be exactly 'allowed' to fall whatever way we please. The quantity of force and energy needed to construct such falls (even if the starting and ending points are the same) will be different. Instead of designing a faulty/incomplete experiment, you can try formulating a straightforward and clear theoretical question. Nonetheless, your question even in its current form appears a bit interesting; only I wish it was clear enough for me to be able to provide you with a better answer/response.
parabolic path would take least time to travel. As the path of diagonal has lesser distance compared to vertical and circular.
dont mind me saying but there are a few things that are missing in this question for example the force with which the ball is being thrown is not mentioned to be constant in all the cases but any way the answer assuming the force is constant will be vertical downwards as it will have acceleration due to gravity to assist it. where as a parabolic motion is noting but throwing the ball up and letting it come down any way i believe the answer is downwards hope i helped.And satish dont mind we saying though the parabolic has least distance only a component of g will act on it thus it will take longer just like throwing a pebble up and down .....