For each natural number k, let `C_k` denotes the circle radius k centimeters in the counter-clockwise direction. After completing its motion on `C_k`, the particle moves to `C_[k+1]` in the radial direction. The motion of the particle continues in this manner. The particle starts at (1,0).If the particle crosses the the positive direction of the x-axis for first time on the circle `C_n`,then n equal to

Answer

n = 7

Explanation

It is given that , `C_(1) " has centre " (0, 0)` and radius 1.
Similarly, `C_(2)` has centre (0, 0) and radius 2 and `C_(k)` ahs centre (0, 0) and radius k.
Now, particle starts it motion from (1, 0) and moves 1 radian on first circle then particle shifts from `C_(1)` to` C_(2)`.
After that, particle moves 1 radian on `C_(2)` and then paricle shifts from `C_(2) " to " C_(3)`. Similarly, particle move on n circles.
Now, `n ge 2pi` because particle crosses the X-axis for the first time on `C_(n)`, then n is least positive integer.
therefore, n = 7.