Discussion
Consider the following statements and choose the incorrect statements:
1. While standard unit of measurement of Kinetic Energy is Watts, Potential energy is measured in Joules.
2. While Kinetic Energy can be positive, negative or zero, Work done cannot be negative.
3. During collision of cars on a non-ideal surface, total Kinetic Energy will necessarily be conserved whether the . collision is elastic or inelastic.
4. During an induction training at Punjab Police Academy, a police officer fires a 23 g bullet (with speed of 11.5 m/sec) on a wooden plank such that the bullet emerges out of the plank with only 50% . of its kinetic energy. In such a case, speed of bullet would also have reduced by 50% after emergence with respect to the speed with which it was fired.
Answer: D
All four statements are incorrect.
1. Kinetic energy and potential energy are both measured in joules; the watt is a unit of power.
2. It is the other way round: kinetic energy, \(\tfrac{1}{2}mv^{2}\), can never be negative, while work can be negative when force opposes displacement.
3. Kinetic energy is conserved only in an elastic collision; in an inelastic one some is turned into heat, sound and deformation.
4. Kinetic energy is proportional to \(v^{2}\), so halving it divides the speed by \(\sqrt{2}\):
\[ \begin{aligned} \tfrac{1}{2}mv'^{2} &= \tfrac{1}{2} \cdot \tfrac{1}{2}mv^{2} \\ v' &= \frac{v}{\sqrt{2}} \approx 0.71v \end{aligned} \]
The speed falls by about 29%, not 50%.
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