For each natural number k,let C_k denote the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The particle starts at $(1, 0)$ on circle $C_1$. On each circle $C_k$,the particle travels an arc length of $k$ cm. The angle subtended by this ar

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) The particle starts at $(1, 0)$ on circle $C_1$. On each circle $C_k$,the particle travels an arc length of $k$ cm. The angle subtended by this arc at the center is $	heta_k = \frac{	ext{arc length}}{	ext{radius}} = \frac{k}{k} = 1$ radian. After completing the motion on $C_k$,the particle moves radially to $C_{k+1}$. Let $	heta_n$ be the total angular position after completing the motion on circle $C_n$. The total angle after $n$ circles is $\sum_{k=1}^{n} 1 = n$ radians. The particle crosses the positive $x$-axis when the total angle is a multiple of $2\pi$. We need the smallest integer $n$ such that $n = 2\pi m$ for some integer $m$. Since $\pi \approx 3.14159$,$2\pi \approx 6.28$. For $n=6$,$6 For $n=7$,$7 > 6.28$. However,the particle moves radially between circles. The angular position remains constant during the radial shift. After completing $C_6$,the total angle is $6$ radians. After completing $C_7$,the total angle is $7$ radians. Since $6 Given the standard interpretation of this problem,the particle crosses the positive $x$-axis for the first time on circle $C_7$.

Similar Questions

If a circle $S$ with radius $5$ touches the circle $x^2+y^2-6x-4y-12=0$ at $(-1,-1)$,then the length of the tangent from the centre of the circle $S$ to the given circle is

The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

Given three collinear points $A(3,1)$,$B(7,-1)$,and $C(5,0)$. The length of a tangent drawn from $A$ to any circle that passes through $B$ and $C$ is ....... units.

If the circles $x^2 + y^2 - 9 = 0$ and $x^2 + y^2 + 2ax + 2y + 1 = 0$ touch each other,then $a =$

If ${c^2} > {a^2}(1 + {m^2})$,then the line $y = mx + c$ will intersect the circle ${x^2} + {y^2} = {a^2}$ at:

Vedclass Test Series

Exam Paper Generator

Online Exam Module