$A$ light spring is suspended with mass $m_1$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $T$ seconds. When a mass $m_2$ is added to $m_1$ and the system is made to oscillate,the period is found to be $\frac{3}{2} T$. The ratio $m_1 : m_2$ is

  • A
    $2:3$
  • B
    $3:4$
  • C
    $4:5$
  • D
    $5:6$

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In the following questions,match Column-$I$ with Column-$II$ and choose the correct options.

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$A$ spring of unstretched length $l$ has a mass $m$ with one end fixed to a rigid support. Assuming the spring to be made of a uniform wire,the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is

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