NEET Exam  >  NEET Questions  >  A wire having a linear mass density 5.0 x 10-... Start Learning for Free
A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will be
  • a)
    1m
  • b)
    4m
  • c)
    4.5m
  • d)
    1.5m
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A wire having a linear mass density 5.0 x 10-3 kg/m is stretched betwe...


View all questions of this test
Most Upvoted Answer
A wire having a linear mass density 5.0 x 10-3 kg/m is stretched betwe...
Free Test
Community Answer
A wire having a linear mass density 5.0 x 10-3 kg/m is stretched betwe...
To find the length of the wire, we can use the formula for the fundamental frequency of a stretched wire:
f = (1/2L) * √(T/μ)

where:
f is the frequency of vibration,
L is the length of the wire,
T is the tension in the wire, and
μ is the linear mass density of the wire.

We are given the following information:
Tension, T = 450 N
Linear mass density, μ = 5.0 x 10^-3 kg/m
Fundamental frequency, f = 400 Hz

Let's substitute these values into the formula and solve for L:

400 = (1/2L) * √(450 / 5.0 x 10^-3)

Simplifying the equation:

400 = (1/2L) * √(9 x 10^4 / 5.0 x 10^-3)

400 = (1/2L) * √(9 x 10^4 x 10^3 / 5.0)

400 = (1/2L) * √(9 x 10^7 / 5.0)

400 = (1/2L) * √(1.8 x 10^7)

Now, to find the length of the wire, we need to solve for L:

L = (1/2) * √(1.8 x 10^7) / 400

L = (0.5) * √(1.8 x 10^7) / 400

L = 0.5 * 4242.64 / 400

L = 2121.32 / 400

L ≈ 5.3033 m

Since the problem asks for the next higher frequency at which the wire resonates, we need to find the length of the wire for a frequency of 500 Hz.

Let's substitute the new frequency into the formula and solve for L:

500 = (1/2L) * √(450 / 5.0 x 10^-3)

Simplifying the equation:

500 = (1/2L) * √(9 x 10^4 / 5.0 x 10^-3)

500 = (1/2L) * √(9 x 10^4 x 10^3 / 5.0)

500 = (1/2L) * √(9 x 10^7 / 5.0)

500 = (1/2L) * √(1.8 x 10^7)

Now, solving for L:

L = (1/2) * √(1.8 x 10^7) / 500

L = (0.5) * √(1.8 x 10^7) / 500

L = 0.5 * 4242.64 / 500

L = 2121.32 / 500

L ≈ 4.2426 m

Since the next higher frequency occurs at 500 Hz, the length of the wire is approximately 4.2426 m. Therefore, the correct answer is option D) 1.5 m.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
Explore Courses for NEET exam

Top Courses for NEET

A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer?
Question Description
A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect 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 wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect 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 wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET. Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A wire having a linear mass density 5.0 x 10-3 kg/m is stretched between two rigid supports with tension of 450 N. The wire resonates at frequency 400 Hz. The next higher frequency at which the wire resonates is 500 Hz. The length of the wire will bea)1mb)4mc)4.5md)1.5mCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev