In a ballistics demonstration, a police officer fires a bullet of mass \(50.0~\text g\) with speed \(200~\text{m/s}\) on soft plywood of thickness \(2.00~\text {cm}.\) The bullet emerges with only \(\text{10%}\) of its initial kinetic energy. The emergent speed of the bullet is:

A block of mass \(m=1\) kg, moving on a horizontal surface with speed \(v_i=\mathrm{2~m/s}\) enters a rough patch ranging from \({x=0.10~\text m}\) to \({x=2.01~\text m}\). The retarding force \(F_r\) on the block in this range is inversely proportional to \(x\) over this range,

\(\begin{aligned} {F}_{r} & =\dfrac{-{k}}{x} \text { for } 0.1<{x}<2.01 {~\text{m}} \\ & =0 \quad ~\text { for } {x}<0.1 \text{ m} \text { and } {x}>2.01 \text{ m} \end{aligned}\)

where \(k=0.5~\text{J}\). What is the final kinetic energy and speed \(v_f\) of the block as it crosses this patch?
1. \(5\) J and \(1\) m/s 
2. \(1\) J and \(5\) m/s
3. \(0.5\) J and \(1\) m/s
4. \(0.05\) J and \(2\) m/s 

A bob of mass m is suspended by a light string of length \(L.\) It is imparted a horizontal velocity \(v_0\) at the lowest point \(A\) such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the ratio of the kinetic energies \(\dfrac{K_B}{K_C}\) ${\mathrm{}}_{}$at points \({B}\) and \({C}\) is:
                       

In a nuclear reactor, a neutron of high speed (typically \(\left(10\right)^{7}\) m/s) must be slowed to \(\left(10\right)^{3}\) m/s so that it can have a high probability of interacting with isotope \(^{235}_{92}U\) and causing it to fission. The material making up the light nuclei, usually heavy water \(\left(D_{2} O\right)\) or graphite, is called a moderator. Find the fraction of the kinetic energy of the neutron lost by it in an elastic collision with light nuclei like deuterium.

1.  \(\dfrac{1}{9}\)

2.  \(\dfrac{8}{9}\)

3.  \(\dfrac{9}{8}\)

4.  \(\dfrac{1}{8}\)