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For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =?
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For each natural number k, let Che denote the circle with radius k cen...
Analysis of Particle Motion on Circles
The motion of the particle on the circles can be analyzed as follows:

Initial Motion on C1
- The particle starts at (1, 0) on the circle C1.
- It moves k centimetres in the counter-clockwise direction on C1.

Motion from Ck to Ck+1
- After completing its motion on Ck, the particle moves to Ck+1 in the radial direction.
- The distance between Ck and Ck+1 is k+1 centimetres.

Intercepting the Positive X-axis
- The particle intercepts the positive direction of the x-axis when it completes a full circle on Cn.
- This means that the sum of the radii of all circles from C1 to Cn is equal to the circumference of Cn.
- Sum of radii = 1 + 2 + 3 + ... + n = n(n+1)/2
- Circumference of Cn = 2πn
- Equating the sum of radii to the circumference, we get n(n+1)/2 = 2πn
- Solving this equation, we get n ≈ 6.28
- Therefore, the particle crosses the positive x-axis for the first time on the circle C6.
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For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =?
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For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =?.
Solutions for For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? defined & explained in the simplest way possible. Besides giving the explanation of For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =?, a detailed solution for For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? has been provided alongside types of For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? theory, EduRev gives you an ample number of questions to practice For each natural number k, let Che denote the circle with radius k centimetres and centre at the origin. 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. The motion of the patticle continues in the 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 =? tests, examples and also practice JEE tests.
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