Two bodies simultaneously begin to move in a circle from one point in one direction.

Two bodies simultaneously begin to move in a circle from one point in one direction. the period of revolution of one body is 3 seconds, the other is 4 seconds. find the minimum period of time after which they will again be at the same point.

Given:

T1 = 3 seconds – the period of movement of the first body in a circle;

T2 = 4 seconds – the period of movement of the second body in a circle.

It is required to determine t (seconds) – the minimum time interval after which the bodies will again appear at one point.

Let the circumference be L (meter).

Then the speed of the first body is equal to:

v1 = L / T1.

The speed of the second body is:

v2 = L / T2.

The speed of the first body relative to the second body is:

v = v1 – v2 = L / T1 – L / T2 = L * (T2 – T1) / (T1 * T1).

It turns out that the bodies will meet again at one point after a time interval equal to:

t = L / v = L / (L * (T2 – T1) / (T1 * T1)) = T1 * T2 / (T2 – T1) = 3 * 4 / (4 – 3) = 12/1 = 12 seconds …

Answer: 12 seconds.