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JEE Main 20178 AprilOnline
Exam
JEE Main
Year
2017
Date
8 April
Mode
Online
Subject
Physics
Chapter
Oscillations

JEE Main 2017 · 8 April · Online · Physics · Oscillations

A 1kg block attached to a spring vibrates with a frequency of 1Hz...

A 1kg1kg block attached to a spring vibrates with a frequency of 1Hz1Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a8kg8kgblock placed on the same table. So, the frequency of vibration of the 8kg8kg block isA 1kg block attached to a spring vibrates with a frequency of 1Hz on a frictionless horizontal table. Two springsA 1kg block attached to a spring vibrates with a frequency of 1Hz on a frictionless horizontal table. Two springs

Options

  1. A2Hz2Hz
  2. B14Hz\dfrac{1}{4}Hz
  3. C122Hz\dfrac{1}{2\sqrt{2}}Hz
  4. D12Hz\dfrac{1}{2}Hz

Correct answer

D. 12Hz\dfrac{1}{2}Hz

Step-by-step solution

A 1kg block attached to a spring vibrates with a frequency of 1Hz on a frictionless horizontal table. Two springs

The frequency of 1kg1kg block is f=12πkm=1Hzf = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}} = 1 Hz

4π2=km,m=14{\pi}^{2} = \dfrac{k}{m},m = 1

Spring constant, k=4π2k = 4{\pi}^{2}

In parallel connection of springs, the equivalent spring constant is keq=2k{k}_{eq} = 2k.

A 1kg block attached to a spring vibrates with a frequency of 1Hz on a frictionless horizontal table. Two springs

f=12πK×28f = \dfrac{1}{2\pi}\sqrt{\dfrac{K \times 2}{8}}

Frequency of 8kg8kg block is=12Hz= \dfrac{1}{2}Hz

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