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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Oscillations

NEET 2016 · Physics · Oscillations

A body of mass, m is attached to the lower end of a spring whose...

A body of mass, mm is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass mm is slightly pulled down and released, it oscillates with a time period of 3s3s. When the mass mm is increased by 1kg1kg, the time period of oscillations becomes 5s5s. The value of mm in kgkg is

Options

  1. A34\dfrac{3}{4}
  2. B43\dfrac{4}{3}
  3. C169\dfrac{16}{9}
  4. D916\dfrac{9}{16}

Correct answer

D. 916\dfrac{9}{16}

Step-by-step solution

T1=3=2πmK{T}_{1} = 3 = 2\pi\sqrt{\dfrac{m}{K}}.

Then, T2=5=2πm+1K{T}_{2} = 5 = 2\pi\sqrt{\dfrac{m + 1}{K}}.

By dividing both the equations, we get,

35=mm+1\dfrac{3}{5} = \sqrt{\dfrac{m}{m + 1}}

925=mm+1\dfrac{9}{25} = \dfrac{m}{m + 1}

9m+9=25m9m + 9 = 25m

16m=916m = 9

m=916m = \dfrac{9}{16}.

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