An elastic spring under tension of $3 \mathrm{~N}$ has a lengtha. Its length is $b$ under tension $2 \mathrm{~N}$. For its length$(3 a-2 b)$, the value of tension will be_______. $\mathrm{N}$.

A block is fastened to a horizontal spring. The block is pulled to a distance $x =10\,cm$ from its equilibrium position (at $x =0$ ) on a frictionless surface from rest. The energy of the block at $x =5$ $cm$ is $0.25\,J$. The spring constant of the spring is $.........Nm ^{-1}$

In stretching a spring by $2\,cm$ energy stored is given by $U,$ then more stretching by $10\,cm$ energy stored will be

A block of mass $2\,\,kg$ is placed on a rough inclined plane as shown in the figure $(\mu  = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The spring will be compressed to a maximum of

A block is attached to a spring as shown and very-very gradually lowered so that finally  spring expands by $"d"$. If same block is attached to spring & released suddenly then maximum expansion in spring will be-

$A$ ball of mass $m = 60gm$ is shot with speed $v_0 = 22m/s$ into the barrel of spring gun of mass $M = 240g$ initially at rest on $a$ frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. The speed of the spring gun after the ball stops relative to the barrel, is