For each natural number k ,let Ck denote the circle with radius k centimeters and centre at the origin O. on the circle Ck a particle moves k centimetres in the counter-clockwise direction. After completing its motion on Ck, the particle moves to Ck+1 in the radial direction (away from centre). The motion of the particle continues in this manner. The particle starts at (1,0). If the particle crosses the positive direction of x-axis for the first time on the circle Cn, then n=

Question

For each natural number k ,let Ck​ denote the circle with radius k centimeters and centre at the origin O. on the circle Ck​ a particle moves k centimetres in the counter-clockwise direction. After completing its motion on Ck​, the particle moves to Ck+1​ in the radial direction (away from centre). The motion of the particle continues in this manner. The particle starts at (1,0). If the particle crosses the positive direction of x-axis for the first time on the circle Cn​, then  n=

Filo · Accepted Answer

The motion of the particle on the first four circles is shown with bold line in the figure

16.22

.
Note that on every circle the particle travels just one radian.
The particle crosses the positive direction of x-axis first time on

C_{n}

,.
where

n

is the least positive integer such that

n > 2 π \Rightarrow n = 7 [n o t e : 2 π \approx 6.28]

.

Question Text	For each natural number $k$ ,let $C_{k}$ denote the circle with radius $k$ centimeters and centre at the origin $O$ . on the circle $C_{k}$ a particle moves $k$ centimetres in the counter-clockwise direction. After completing its motion on $C_{k}$ , the particle moves to $C_{k + 1}$ in the radial direction (away from centre). The motion of the particle continues in this manner. The particle starts at $(1, 0)$ . If the particle crosses the positive direction of x-axis for the first time on the circle $C_{n}$ , then $n =$
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