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Byju's Answer

Standard XII

Physics

Introduction

If k belong...

Question

If $k$ belongs to set of natural numbers and $l = R$ particle moves tangentially from the circle $C_{k}$ to $C_{k + 1}$ such that the length of tangent is equal to $k$ units itself.If particle starts from the point $(1, 0)$ then

the particle will cross

x -

axis again at

x = 3

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the particle will cross

x -

axis again at

x = 4

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the particle will cross

x -

axis again at

x = 2 \sqrt{2}

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the particle will cross

x -

axis again at

x \in (2 \sqrt{2}, 4)

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Solution

The correct option is D the particle will cross $x -$ axis again at $x \in (2 \sqrt{2}, 4)$
Write calculation the angular distance from starting of motion.
The distance for one circle to reach to other is
$1 + \frac{π}{4} \approx 57^{\circ} 17^{'} 48^{''} + 45 ° \approx 102 ° 17^{'} {44.8}^{''}$ and to cover x-axis again should cover $π$ radian.
$∴ (\frac{π^{c}}{1^{c}}) = π^{c}$
On $4^{t h}$ circle particle will cross the positive x−axis again.
Where $x ϵ$ $(2 \sqrt{2}, 4)$

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If k belongs to set of natural numbers and l=R particle moves tangentially from the circle Ck to Ck+1 such that the length of tangent is equal to k units itself.If particle starts from the point (1,0) then

If $k$ belongs to set of natural numbers and $l = R$ particle moves tangentially from the circle $C_{k}$ to $C_{k + 1}$ such that the length of tangent is equal to $k$ units itself.If particle starts from the point $(1, 0)$ then