Question

Referring the graphs, which of the following is/are correct?

• A. The particle has stable equilibrium at points 3 and b.
• B. The particle is in neutral equilibrium at points b and 2 .
• C. No power is delivered by the force on the particle at points 1,3 , and b.
• D. The particle has least kinetic energy at position 1 .

Answer 1

Answer: (A), (C), (D)

Option (1) is correct because at 3 , force is opposite to displacement.
At $b, u$ is minimum.
Option (2) is incorrect because at 2 , there is net force and hence no equilibrium.
Option (3) is correct because at 1,3 and $b$ force is zero.
At $b, \frac{d u}{d x}=-F=0$
Option (4) is correct. Positive work is done after position 1.
Hence, $KE$ will increase. So $KE$ is least at 1 .