0

Guest

Courses New

Three particles located initially on the vertices of an equilateral triangle of side L, start moving with a constant tangential acceleration towards each other in a cyclic manner, forming spiral loci that coverage at the centroid of the triangle. The length of one such spiral locus will be ?

Three particles located initially on the vertices of an equilateral triangle of side L, start moving with a constant tangential acceleration towards each other in a cyclic manner, forming spiral loci that coverage at the centroid of the triangle. The length of one such spiral locus will be ?

Grade:12

1 Answers

Vasanth SR
askIITians Faculty 1335 Points
6 years ago
Symmetry is your friend here. Whatever happens to the three points at any point in time, it should look exactly the same if you rotate the whole thing by 120 degrees. This is the key to solving the problem.
Let's think about what things should look like at some timetafter they start moving. All three points were initially at the same distance from the centroid of the original equilateral triangle of sideA(the point which is equidistant from all three vertices), so at timet, wherever the points are, they are still at the same distance from the centroid, and the rotational symmetry is still preserved. This should convince you that the three points remain as an equilateral triangle even as they move around.
This means that at any timet, if you take a snapshot of the three points, they still form an equilateral triangle, moving with the same speed and in the same manner.Aside from the length of this equilateral triangle, this is identical to the initial problem. At any timet,in other words, the distance between two points is decreasingat the same rate as at the beginning.
So to find the total amount of time taken for the points to meet, we simply takeAdivided by the initial rate at which two points approach each other. Pick any two points, and you can see that the first point moves in the direction of the second at speedv, while the second moves in the direction of the first (just take the component along one of the triangle edges) atv cos 60 = v/2. Therefore, the rate at which the distance between the two points is decreasing is3v/2.
The time taken for the three points to meet is thus2A/3v.

Think You Can Provide A Better Answer ?

Other Related Questions on IIT JEE Entrance Exam

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More