Q121 / 180 · AIIMS 2004 · Physics

Two springs are connected to a block of mass $M$ placed on a frictionless surface as shown in the figure. If both the springs have a spring constant $k$, the frequency of oscillation of the block is Figure

  • A
    $\frac{1}{2 \pi} \sqrt{\frac{k}{M}}$
  • Correct answer
    B
    $\frac{1}{2 \pi} \sqrt{\frac{k}{2 M}}$
  • C
    $\frac{1}{2 \pi} \sqrt{\frac{2 k}{M}}$
  • D
    $\frac{1}{2 \pi} \sqrt{\frac{M}{k}}$.

Solution

The spring constant of spring connected in series is equal to $$ k_s=\frac{k_1 k_2}{k_1+k_2}=\frac{k}{2}\left(F_{\text {or }} k=k_2=k\right) $$ Thus frequency of oscillation of given system is $$ f=\frac{1}{2 \pi} \sqrt{\frac{k}{2 m}} $$

Hence, the correct answer is option: 'B'.

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