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A mass m is suspended from a string of length l and force constant K. The frequency of vibration of the mass is f₁. The spring is cut into two equal Parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is f₂. Which of the following relations between the frequencies is correct
  • a)
    f₁ = √2 f₂
  • b)
    f₁=2f₂
  • c)
    f₁ = 2f₂
  • d)
    f₂ = √2 f₁
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A mass m is suspended from a string of length l and force constant K. ...

Sure. The answer is d) f₂ = √2 f₁.

The frequency of vibration of a mass suspended from a spring is given by

f = 1/(2π) * sqrt(k/m)
where k is the force constant of the spring and m is the mass of the suspended object.

When the spring is cut into two equal parts, the force constant of each part is k/2. The frequency of vibration of the mass suspended from one of the parts is then given by

f₂ = 1/(2π) * sqrt((k/2)/m) = 1/(2π) * sqrt(k/(2m)) = sqrt(2) * f₁
Therefore, the correct relation between the frequencies is f₂ = √2 f₁.

Here is the explanation of the formula for the frequency of vibration of a mass suspended from a spring:

The frequency of vibration of a mass suspended from a spring is the number of times per second that the mass passes through its equilibrium position. The period of vibration is the time it takes for the mass to pass through its equilibrium position once. The frequency of vibration is the inverse of the period of vibration.

The period of vibration of a mass suspended from a spring is given by

T = 2π * sqrt(m/k)
where m is the mass of the suspended object and k is the force constant of the spring.

The frequency of vibration is then given by

f = 1/T = 1/(2π) * sqrt(k/m)
As you can see, the frequency of vibration is proportional to the square root of the force constant of the spring and inversely proportional to the square root of the mass of the suspended object.
Community Answer
A mass m is suspended from a string of length l and force constant K. ...
F
b)f = 2f
c)f = f/2
d)f = √2f
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A mass m is suspended from a string of length l and force constant K. The frequency of vibration of the mass is f₁. The spring is cut into two equal Parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is f₂. Which of the following relations between the frequencies is correcta)f₁ = √2 f₂b)f₁=2f₂c)f₁ = 2f₂d)f₂ = √2 f₁Correct answer is option 'D'. Can you explain this answer?
Question Description
A mass m is suspended from a string of length l and force constant K. The frequency of vibration of the mass is f₁. The spring is cut into two equal Parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is f₂. Which of the following relations between the frequencies is correcta)f₁ = √2 f₂b)f₁=2f₂c)f₁ = 2f₂d)f₂ = √2 f₁Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass m is suspended from a string of length l and force constant K. The frequency of vibration of the mass is f₁. The spring is cut into two equal Parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is f₂. Which of the following relations between the frequencies is correcta)f₁ = √2 f₂b)f₁=2f₂c)f₁ = 2f₂d)f₂ = √2 f₁Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass m is suspended from a string of length l and force constant K. The frequency of vibration of the mass is f₁. The spring is cut into two equal Parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is f₂. Which of the following relations between the frequencies is correcta)f₁ = √2 f₂b)f₁=2f₂c)f₁ = 2f₂d)f₂ = √2 f₁Correct answer is option 'D'. Can you explain this answer?.
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