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 velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$

The springs in figure. $A$ and $B$ are identical but length in $A$ is three times that in $B$. The ratio of period $T_A/T_B$ is

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

The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.

If a spring has time period $T$, and is cut into $n$ equal parts, then the time period of each part will be

In an elevator, a spring clock of time period $T_S$ (mass attached to a spring) and a pendulum clock of time period $T_P$ are kept. If the elevator accelerates upwards