Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that E mech = 8 J, the incorrect statement for this system is :
[ where K.E. = kinetic energy ]

Solution

Physics sir · 3 steps

Kinetic energy is the gap between the 8 J line and the curve, so read that gap in each region.

1. Energy conservation. The force is conservative, so the total mechanical energy stays at 8 J everywhere. At any point, the kinetic energy is what is left after the potential energy is taken out.

   K = E_(mech) - U(x) = 8 J - U(x)

   Option	U from the graph	K = 8 - U	Statement is
   (a) x > x₄	flat at 6 J	2 J, the same all along	true
   (b) x < x₁	flat at 8 J	0 J, so the particle is at rest	incorrect
   (c) x = x₂	0 J, the lowest point	8 J, the largest value	true
   (d) x = x₃	4 J	4 J	true

2. Why (b) fails. For x < x₁ the curve touches the 8 J line, so K = 0 there. The particle is not moving at all. It is not moving at a small speed. The slope there is also zero, so no force acts to set it moving.
3. So. Statements (a), (c) and (d) agree with K = 8 - U. The incorrect statement is (b).

The idea to keep. On a U–x graph, K.E. is the vertical gap from the energy line down to the curve. Where that gap is zero, K.E. is zero and the particle is at rest. It is not moving slowly.

Answer from the NTA final answer key. Solution by PrepWiser.