Question

For each $kϵN$, let $C_k$ denote the circle whose equation is $x^2+y^2=k^2$. On the circle $C_k$, a particle moves $k$ units in the anticlockwise 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 crossed the positive direction of the $x$-axis for the first time of the circle $C_n$ then $n$ is:

• A. $7$
• B. $6$
• C. $2$
• D. none of these

Answer 1

The correct option is A $7$

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 $n>2\pi \Rightarrow n=7$.