The block $A$ is pushed towards the wall by a distance $x$ and released. The normal reaction $N$ by the vertical wall on the block $B$ versus the compression $x$ in the spring is given by:

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

Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is

$A$ 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 $N$)

The force constant of a spring is $K$. If half of the spring is cut off,what will be the force constant of the remaining spring?

Two balls $A$ and $B$ of masses $100 \ gm$ and $250 \ gm$ are connected by a stretched massless spring and placed on a smooth table. When the balls are released simultaneously,the initial acceleration of ball $B$ is $10 \ cm/s^2$ towards the west. Find the magnitude and direction of the initial acceleration of ball $A$.