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_______. $\mathrm{N}$.

 spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring some elongation and released. the block will have maximum velocity when

Write the dimensional formula of $\frac {k}{m}$.

Two blocks $A$ and $B$ of mass $m$ and $2\, m$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. Spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is :-

In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiency large. Consider the spring constant to be $K$.

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-