Question

Two particles interact by conservative forces and no other forces act. They complete a round trip ending at the points where they started. For this round-trip mark out the incorrect statement(s)

• A. The total KE might have a different value at the beginning, and at the end.
• B. The total PE might have a different value at the beginning, and at the end.
• C. The total mechanical energy might have a different value at the beginning, and at the end.
• D. The total mechanical energy might have a same value at the beginning, and at the end.

Answer 1

Answer: (A), (B), (C)

The total mechanical energy might have a different value at the beginning, and at the end.

1. Kinetic energy is given by,
   $K.E.=\frac{1}{2}m{v}^2$
2. Potential energy is given by,
   $P.E.=mgh$
3. Total mechanical energy of a system is the sum of kinetic energy and potential energy.
4. In a conservative field,
5. Total mechanical energy is conserved. Hence option c is incorrect.
6. Potential energy depends on the position of a particle. Particles return to the same position after the trip ends. Hence, potential energy remains the same. So, option b is incorrect.
7. As total energy is conserved,
   ${\left(K.E+P.E\right)}_i={\left(K.E+P.E\right)}_f$
   Potential energy remains the same. Hence, kinetic energy also remains conserved. This means that option a is incorrect.

Final Answer: Option (a), (b) and (c)