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AIIMS 2010
Exam
AIIMS
Year
2010
Subject
Physics
Chapter
Laws of Motion

AIIMS 2010 · Physics · Laws of Motion

Let T_1 and T_2 be the time periods of springs A and B when mass M...

Let T1T_1 and T2T_2 be the time periods of springs AA and BB when mass MM is suspended from one end of each spring. If both springs are taken in series and the same mass MM is suspended from the series combination, the time period is TT, then

Options

  1. AT1+T2+T3T_1+T_2+T_3
  2. B1T=1T1+1T2\frac{1}{T}=\frac{1}{T_1}+\frac{1}{T_2}
  3. CT2=T12+T22T^2=T_1^2+T_2^2
  4. D1T2=1T12+1T2\frac{1}{T^2}=\frac{1}{T_1^2}+\frac{1}{T^2}

Correct answer

C. T2=T12+T22T^2=T_1^2+T_2^2

Step-by-step solution

T1=2πMk1T_1=2 \pi \sqrt{\frac{M}{k_1}} or k1=4π2MT12k_1=\frac{4 \pi^2 M}{T_1^2} and k2=4π2MT22k_2=\frac{4 \pi^2 M}{T_2^2} In series combination, keff =k1k2k1+k2=4π2MT12+T22k_{\text{eff }}=\frac{k_1 k_2}{k_1+k_2}=\frac{4 \pi^2 M}{T_1^2+T_2^2} \therefore T=2 πMkeff=T12+T22. \pi \sqrt{\frac{M}{k_{\mathrm{eff}}}}=\sqrt{T_1^2+T_2^2} \text{. }
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