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JEE Main 202124 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Evening Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2021 · 24 February · Evening Shift · Physics · Oscillations

In the given figure, a body of mass M is held between two massless...

In the given figure, a body of mass MM is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k,k, the frequency of oscillation of given body is:

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends

Options

  1. A12π2kMgsinα\dfrac{1}{2\pi}\sqrt{\dfrac{2k}{Mgsin\alpha}}
  2. B12πkMgsinα\dfrac{1}{2\pi}\sqrt{\dfrac{k}{Mg}sin\alpha}
  3. C12πk2M\dfrac{1}{2\pi}\sqrt{\dfrac{k}{2M}}
  4. D12π2kM\dfrac{1}{2\pi}\sqrt{\dfrac{2k}{M}}

Correct answer

D. 12π2kM\dfrac{1}{2\pi}\sqrt{\dfrac{2k}{M}}

Step-by-step solution

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends

Keq=K1+K2=K+K=2K{K}_{eq} = {K}_{1} + {K}_{2} = K + K = 2K

T=2πmKeq=2πm2KT = 2\pi\sqrt{\dfrac{m}{{K}_{eq}}} = 2\pi\sqrt{\dfrac{m}{2K}}

f=1T=12π2Kmf = \dfrac{1}{T} = \dfrac{1}{2\pi}\sqrt{\dfrac{2K}{m}}

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