The force constants of two springs are ${K_1}$ and ${K_2}$. Both are stretched till their elastic energies are equal. If the stretching forces are ${F_1}$ and ${F_2}$, then ${F_1}:{F_2}$ is

A man weighing $60\, kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\, m$ and frequency $\frac{2}{\pi }Hz$. Which of the following statement is correct

The angular frequency of a spring block system is $\omega _0.$ This system is suspended from the ceiling of an elevator moving downwards with a constant speed $v_0.$ The block is at rest relative to the elevator. Lift is suddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement :

Two small bodies of mass of $2\, kg$ each attached to each other using a thread of length $10\, cm$, hang on a spring whose force constant is $200\, N/m$, as shown in the figure. We burn the thread. What is the distance between the two bodies when the top body first arrives at its highest position …. $cm$ ? (Take $\pi^2 = 10$)

A mass $M$, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\frac{{{A_1}}}{{{A_2}}}$ is