Two bodies $M$ and $N $ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude $M$ to that of $N$ is
$\frac{{{k_1}}}{{{k_2}}}$
$\sqrt {\frac{{{k_1}}}{{{k_2}}}} $
$\frac{{{k_2}}}{{{k_1}}}$
$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $
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 block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact is
The vertical extension in a light spring by a weight of $1\, kg$ suspended from the wire is $9.8\, cm$. The period of oscillation
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor. The time for which rear moving block remain in contact with spring will be ... $\sec$
A weightless spring of length $60\, cm$ and force constant $200\, N/m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25\, kg$ is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is