A body is moving with constant speed, in a circle of radius 20 m. The body completesone revolution in4 s. At the end of 3rd second, find the displacement of body (in m) from its starting poin

To solve this problem, we need to understand that displacement is the shortest distance from the initial to the final position of a point. Thus, for a circular path, the displacement is the straight line joining the initial and final points.

Here are the steps to find the displacement:

1. First, we need to find the angle covered by the body in 3 seconds. We know that the body completes one revolution (360 degrees) in 4 seconds. Therefore, in 1 second, the body covers 360/4 = 90 degrees. So, in 3 seconds, the body will cover 3*90 = 270 degrees.

2. Now, we need to convert this angle from degrees to radians because the formula to calculate displacement in circular motion uses radians. We use the conversion factor π rad = 180 degrees. So, 270 degrees = 270*(π/180) = 3π/2 radians.

3. The formula for displacement in circular motion is d = 2r*sin(θ/2), where r is the radius of the circle and θ is the angle covered in radians. Substituting the given radius r = 20 m and the calculated θ = 3π/2 radians into the formula, we get:

   d = 220sin((3π/2)/2) = 40*sin(3π/4).

4. Using the known value sin(3π/4) = √2/2, the displacement d = 40*√2/2 = 20√2 m.

So, the displacement of the body from its starting point at the end of the 3rd second is 20√2 meters.