The graph shown was obtained from experimental measurements of the period of oscillations $T$ for different masses $M$ placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the

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 ..... $m/s$

Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\, rad/s$, and amplitude $1.6\, cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... $N$ ( take $g = 10\, ms^{-2}$)

On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $K$, the period of oscillation of the body (assuming the springs as massless) is

As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$

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