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Answer:
It is given that on the circle Ck of radius kcm, the particle moves kcm.
Therefore, angular displacement (θ) on kth circle is given by- θ= radius
distance travelled by the particle =kk radian=1 radian
Thus angular displacement on each circle is 1 radian.
If the particle crosses the x-axis for the first time on circle Cn
, then-
Total angular displacement =n radians, i.e.,
We have to move to the circle with radius n to cover the angle of2πn .
∴n>2π
Since n is the natural number such that n>2π.
∴n=7
Hence the required answer is n=7.
THE REQUIRED ANSWER IS N=7