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For each natural number k,let Ck denotes the circle with radius k cm and centre at origin.on the circle Ck,a particle moves k cm in the counter clockwise direction.after completing it's motion on Ck, the particle moves onCk+1in the radial direction.the motion of the particle continues in this manner.the particle starts at (1,0).if the particle crosses the positive direction of the x-axis for the first time on the circle Cn,then n is equal to

 

Asked by azizrajil03 7th December 2018, 6:59 AM
Answered by Expert
Answer:
Every time the particle moves k cm in a circle Ck which has radius k cm.
Hence angular displacement made by the particle when it travel on each circle is 1 radian ( angle in radian = Arc Length divided by radius)
 
Particle starts from (1,0). It has started from X-axis and travelling first time on circle C1 .
After travelling 1 cm or 1 radian in angular direction it moves radially to Circle  C2 and so on.
To cross positive direction of X-axis, required angular displacement is 2π radians (≈ 6.28 radians ).
Hence after 6 radians particle will move to C7 .
Hence when it travels on C7 it will cross positive direction of x-axis. Hence answer to this question is n = 7
Answered by Expert 7th December 2018, 11:01 AM
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