The springs shown are identical. When $A = 4kg$, the elongation of spring is $1\, cm$. If $B = 6\,kg$, the elongation produced by it is  ..... $ cm$

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 ..... $m/s$

A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be

Two springs of constant ${k_1}$and ${k_2}$are joined in series. The effective spring constant of the combination is given by

A block whose mass is $1 \;kg$ is fastened to a spring. The spring has a spring constant of $50\; N m ^{-1}$. The block is pulled to a distance $x=10\; cm$ from its equilibrlum position at $x=0$ on a frictionless surface from rest at $t=0 .$ Calculate the kinetic, potentlal and total energles of the block when it is $5 \;cm$ away from the mean position.

A $5\, kg$ collar is attached to a spring of spring constant $500\, Nm^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equillibrium position by $10\, cm$ and released. The time period of oscillation is