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Maths-

General

Easy

Question

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

$3 : 1$
$1 : 3$
$1 : 2$
$2 : 1$

hint Hint:

We know that, $s equals R theta$ [s= arc length, R= radius, $theta$ = angle subtended at the center]. We can solve the question with this equation.

The correct answer is: $3 colon 1$

Step by step solution:
Given that,
$theta subscript 1 equals 25 degree$
$theta subscript 2 equals 75 degree$
It is also given that $s subscript 1 equals s subscript 2$
We know that $s equals R theta$
$s subscript 1 equals space R subscript 1 theta subscript 1$
$s subscript 2 equals R subscript 2 theta subscript 2$
$s subscript 1 equals s subscript 2$
$rightwards double arrow R subscript 1 space end subscript left parenthesis 25 degree right parenthesis equals R subscript 2 left parenthesis 75 degree right parenthesis$
$rightwards double arrow R subscript 1 over R subscript 2$ $equals 3 over 1$
$rightwards double arrow R subscript 1 colon R subscript 2 equals 3 colon 1$ (answer)
Hence, option(b) is the correct option.

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