Mention the work done by spring force in cylic process.

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slowing down of neutrons: In a nuclear reactor a neutron of high speed (typically $10^{7}\; m s ^{-1}$ ) must be slowed to $10^{3}\; m s ^{-1}$ so that it can have a high probability of interacting with isotope $^{235} _{92} U$ and causing it to fission. Show that a neutron can lose most of its kinetic energy In an elastic collision with a light nuclel like deuterlum or carbon which has a mass of only a few times the neutron mass. The material making up the light nuclel, usually heavy water $\left( D _{2} O \right)$ or graphite, is called a moderator.

A block $(B)$ is attached to two unstretched springs $\mathrm{S} 1$ and $\mathrm{S} 2$ with spring constants $\mathrm{k}$ and $4 \mathrm{k}$, respectively (see figure $\mathrm{I}$ ). The other ends are attached to identical supports $M1$ and $M2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $\mathrm{B}$ is displaced towards wall $1$ by a small distance $\mathrm{x}$ (figure $II$) and released. The block returns and moves a maximum distance $\mathrm{y}$ towards wall $2$ . Displacements $\mathrm{x}$ and $\mathrm{y}$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is Figure: $Image$

  • [IIT 2008]

A spring $40\,mm$ long is stretched by the application of a force. If $10\, N$ force is required to stretch the spring through $1\, mm$, then work done in stretching the spring through $40\, mm$ is ............. $\mathrm{J}$

A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$. Initially the spring is in its natural length. Velocity of the container at the instant compression in spring is maximum for the first time :-
 

A ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$ . Other end of spring is fixed and ring can slide on a smooth horizontal rod as shown. Now the ring is shifted to position $B$ and released, speed of ring when spring attains it's natural length is