The springs shown in the figure are identical,each having a spring constant $K$. When mass $A = 4\, kg$ is attached,the elongation of the spring is $1\, cm$. If mass $B = 6\, kg$ is attached to the system of two springs in series as shown,the total elongation produced is ..... $cm$.

$A$ mass of $2.0\, kg$ is placed on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released,the mass executes simple harmonic motion. The spring constant is $200\, N/m$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan? (Take $g = 10\, m/s^2$)

If a vertical mass-spring system is taken to the moon,what will happen to its time period?

Two springs of force constants $300 \, N/m$ (Spring $A$) and $400 \, N/m$ (Spring $B$) are joined together in series. The combination is compressed by $8.75 \, cm$. The ratio of energy stored in $A$ and $B$ is $E_A / E_B$. Then $E_A / E_B$ is equal to:

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring,such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released,it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be

$A$ uniform circular disc of mass $12 \ kg$ is held by two identical springs. When the disc is slightly pressed down and released,it executes $S.H.M.$ of period $2 \ s$. The force constant of each spring is (nearly) (Take $\pi^2=10$) (in $Nm^{-1}$)