When the acceleration of the $5\ kg$ block is $2\ m/s^2$ as shown in the figure,what will be the acceleration of the $15\ kg$ block? (in $m/s^2$)

Infinite springs with force constants $k$,$2k$,$4k$,$8k$,... respectively are connected in series. The effective force constant of the system will be:

$A$ massless spring gets elongated by an amount $x_1$ under a tension of $5 \ N$. Its elongation is $x_2$ under a tension of $7 \ N$. For an elongation of $(5x_1 - 2x_2)$,the tension in the spring will be: (in $N$)

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

In the figure,blocks $A$ (mass $2m$) and $B$ (mass $m$) are connected with a string and the system is suspended vertically with the help of a spring. The spring has negligible mass. Find the magnitude of the acceleration of masses $2m$ and $m$ just after the instant when the string is cut.

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length,the line $OA$ will