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A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in between
- a)0 and 1/2
- b)1/2 and 1
- c)- 1 / 2 to 0
- d)- 1 t o - 1 / 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A ring of diameter 10 cm is suspended from a point 12 cm vertically ab...
Consider the problem as a pyramid to the base of a regular hexagon.
Now in A POR
Now in A POR
OP = 12 cm
OR = 5 cm
PR = 13 cm
Now cosine formula will give the answer.
Most Upvoted Answer
A ring of diameter 10 cm is suspended from a point 12 cm vertically ab...
Given:
Diameter of the ring = 10 cm
Vertical distance between the point of suspension and the centre of the ring = 12 cm
Number of strings suspending the ring = 6
To find: The range of cosine of the angle between two adjacent strings
Solution:
Let's consider the ring and the point of suspension and draw a diagram.
As shown in the diagram, let's consider two adjacent strings and draw a triangle using the vertical distance between the point of suspension and the centre of the ring (12 cm), the radius of the ring (5 cm), and the line connecting the point of suspension and the point of attachment of one of the strings on the circumference of the ring.
Now, using the cosine formula, we can find the cosine of the angle between the two adjacent strings.
cos(θ) = (12^2 + 5^2 - 5^2) / (2 * 12 * 5)
cos(θ) = 119 / 120
Therefore, the cosine of the angle between two adjacent strings is 119/120.
To find the range, let's simplify the cosine value by dividing both numerator and denominator by 5.
cos(θ) = 24/25
As we know, cosine values lie between -1 and 1.
-1 ≤ cos(θ) ≤ 1
Multiplying both sides of the inequality by 25, we get:
-25 ≤ 24cos(θ) ≤ 25
Adding 24 to all sides of the inequality, we get:
-1 ≤ 24cos(θ) + 24 ≤ 24
Dividing all sides of the inequality by 24, we get:
-1/24 ≤ cos(θ) + 1/24 ≤ 1
Therefore, the range of cosine of the angle between two adjacent strings lies between 1/24 and 25/24.
Simplifying further, we get:
1/24 < cos(θ)="" />< />
Therefore, the correct option is B) 1/2 and 1.
Diameter of the ring = 10 cm
Vertical distance between the point of suspension and the centre of the ring = 12 cm
Number of strings suspending the ring = 6
To find: The range of cosine of the angle between two adjacent strings
Solution:
Let's consider the ring and the point of suspension and draw a diagram.
As shown in the diagram, let's consider two adjacent strings and draw a triangle using the vertical distance between the point of suspension and the centre of the ring (12 cm), the radius of the ring (5 cm), and the line connecting the point of suspension and the point of attachment of one of the strings on the circumference of the ring.
Now, using the cosine formula, we can find the cosine of the angle between the two adjacent strings.
cos(θ) = (12^2 + 5^2 - 5^2) / (2 * 12 * 5)
cos(θ) = 119 / 120
Therefore, the cosine of the angle between two adjacent strings is 119/120.
To find the range, let's simplify the cosine value by dividing both numerator and denominator by 5.
cos(θ) = 24/25
As we know, cosine values lie between -1 and 1.
-1 ≤ cos(θ) ≤ 1
Multiplying both sides of the inequality by 25, we get:
-25 ≤ 24cos(θ) ≤ 25
Adding 24 to all sides of the inequality, we get:
-1 ≤ 24cos(θ) + 24 ≤ 24
Dividing all sides of the inequality by 24, we get:
-1/24 ≤ cos(θ) + 1/24 ≤ 1
Therefore, the range of cosine of the angle between two adjacent strings lies between 1/24 and 25/24.
Simplifying further, we get:
1/24 < cos(θ)="" />< />
Therefore, the correct option is B) 1/2 and 1.
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A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer?
Question Description
A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer?.
A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer?.
Solutions for A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A ring of diameter 10 cm is suspended from a point 12 cm vertically above the centre by six equal strings. The strings are attached to the circumference of the ring at equal intervals, thus keeping the ring in a horizontal plane. The value of cosine of the angle between the two adjacent strings lies in betweena)0 and 1/2b)1/2 and 1c)- 1 / 2 to 0d)- 1 t o - 1 / 2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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