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Oscillations question

2016 · Q158
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Oscillations question

2016 · Q158

NEETPhysicsOscillationsMCQ+4 / −1
A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is
  1. A
    34{3 \over 4}43​
  2. B
    43{4 \over 3}34​
  3. C
    169{{16} \over 9}916​
  4. D
    916{9 \over {16}}169​
View written solutionFree

Correct answer: D

The time period of oscillation is given by

T=2πm/kT = 2\pi \sqrt {m/k} T=2πm/k​

T1=3=2πm/k{T_1} = 3 = 2\pi \sqrt {m/k} T1​=3=2πm/k​

T2=5=2π(m+1k){T_2} = 5 = 2\pi \sqrt {\left( {{{m + 1} \over k}} \right)} T2​=5=2π(km+1​)​

On dividing :

3/5=m/(m+1)3/5 = \sqrt {m/\left( {m + 1} \right)} 3/5=m/(m+1)​

9/25=m/(m+1)9/25 = \sqrt {m/\left( {m + 1} \right)} 9/25=m/(m+1)​

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

16m=9⇒m=9/1616m = 9 \Rightarrow m = 9/1616m=9⇒m=9/16

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