In a spring gun having spring constant $100\, {N} / {m}$ a small ball $'B'$ of mass $100\, {g}$ is put in its barrel (as shown in figure) by compressing the spring through $0.05\, {m}$. There should be a box placed at a distance $'d'$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2\, {m}$ above the ground. The value of $d$ is $....{m} .$ $\left(g=10\, {m} / {s}^{2}\right)$

A block $C$ of mass $m$ is moving with velocity $v_0$ and collides elastically with block $A$ of mass $m$ which connected to another block $B$ of mass $2\,m$ through a spring of spring constant $k$. What is $k$ if $x_0$ is the compression of spring when velocity of $A$ and $B$ is same?

A ball of mass $4\, kg$, moving with a velocity of $10\, ms ^{-1}$, collides with a spring of length $8\, m$ and force constant $100\, Nm ^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$, to the nearest integer, is ........ .

A ball of mass $100 \,g$ is dropped from a height $h =$ $10\, cm$ on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{ h }{2}$. The spring constant is.......... $Nm^{-1}$ . (Use $g=10\, ms ^{-2}$ )

$A$ small block of mass $m$ is placed on $a$ wedge of mass $M$ as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down, then  Maximum retardation of $M$ is:

A spring of force constant $k$ is cut in two parts at its one third length. When both the parts are stretched by same amount, the work done in the two parts, will be