What is the acceleration of $3 \,kg$ mass when the acceleration of $2 \,kg$ mass is $2 \,m/s^2$ as shown in the figure? (in $m/s^2$)

Natural length of a spring is $60\, cm$,and its spring constant is $4000\, N/m$. $A$ mass of $20\, kg$ is hung from it. The extension produced in the spring is,.......$cm$ (Take $g = 9.8\, m/s^2$)

$A$ light spring of length $20 \ cm$ and force constant $2 \ kg/cm$ is placed vertically on a table. $A$ small block of mass $1 \ kg$ falls on it. The height $h$ from the surface of the table at which the block will have the maximum velocity is ............... $cm$.

$A$ body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1\, cm$. If the angular velocity is doubled,the elongation in the spring is $5\, cm$. The original length of the spring is ......... $cm$

$A$ spring has length $l$ and force constant $K$. If it is cut into two springs of length $l_1$ and $l_2$ such that $l_1 = n l_2$ ($n$ is an integer). The force constant of the spring of length $l_2$ is

$A$ spring of force constant $k$ is cut into two equal halves. The force constant of each half is