In a ballistics demonstration, a police officer fires a bullet of mass \(50.0\) g with speed \(200\) m/s on soft plywood of thickness \(2.00\) cm. The bullet emerges with only \(\text{10%}\) of its initial kinetic energy. The emergent speed of the bullet is:
1. | \(0\) | 2. | \(53.2\) m/s |
3. | \(63.2\) m/s | 4. | \(6.32\) m/s |
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 \(\dfrac{K_B}{K_C}\) at points \({B}\) and \({C}\) is:
1. | \(1:3\) | 2. | \(3:1\) |
3. | \(1:5\) | 4. | \(5:1\) |
1. | straight line | 2. | circular |
3. | projectile | 4. | can't be determined |
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. \(\dfrac{1}{8}\)