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

A spring of force constant $800\, N/m$ has an extension of $5\,cm$. The work done in extending it from $ 5\,cm$ to $15 \,cm$ is ............. $\mathrm{J}$

A spring is compressed between two blocks of masses $m_1$ and $m_2$  placed on a horizontal frictionless surface as shown in the figure. When the blocks arc released, they have initial velocity of $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest. The ratio $\left( {\frac{{{x_1}}}{{{x_2}}}} \right)$ is

A toy gun fires a plastic pellet with a mass of $0.5\  g$. The pellet is propelled by a spring with a spring constant of $1.25\  N/cm$, which is compressed $2.0\  cm$ before firing. The plastic pellet travels horizontally $10\  cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\  N$. What is the speed (in $SI\  units$) of the bullet as it emerges from the barrel?

A massless platform is kept on a light elastic spring as shown in fig. When a sand particle of mass $0.1\; kg$ is dropped on the pan from a height of $0.24 \;m$, the particle strikes the pan and spring is compressed by $0.01\; m$.

From what height should the particle be dropped to cause a compression of $0.04\; m$.

A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k.$ The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be