It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass \(1.00\) g falling from a height of \(1.00\) km. It hits the ground with a speed of \(50.0\) m/s. Work done by the gravitational force and work done by the unknown resistive force respectively are:

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.  \(\dfrac{1}{8}\)