Question

The given plot shows the variation of U, the potential energy of interaction between two particles with the distance separating them be $r$, then which of the following is correct?
(1) B and D are equilibrium points
(2) C is a point of stable equilibrium
(3) The force of interaction between the two particles is attractive between points C and D and repulsive between points D and E on the curve.
(4) The force of interaction between the particles is repulsive between points E and F on the curve.

• A. 1 and 3
• B. 1 and 4
• C. 2 and 4
• D. 2 and 3

Answer 1

The correct option is C 2 and 4

$weknowthatdU=-\overrightarrow{F}\cdot \overrightarrow{dr}\Rightarrow F=-\frac{dU}{dr}ForequilibriumpositionF=0\Rightarrow \frac{dU}{dr}=0So,pointCistheequilibriumpositionAlso\frac{d^{2}U}{d{x}^2}>0atpointC,ThereforepointCisthepointofstableequilibriumbetweenDandE,dU>0\Rightarrow -\overrightarrow{F}\cdot \overrightarrow{dr}>0\Rightarrow \overrightarrow{F}\cdot \overrightarrow{dr}<0\Rightarrow Both\overrightarrow{F}and\overrightarrow{dr}areinoppositedirectionThereforebetweenDandEforceisattractiveSimilarly,betweenpointsEandF\overrightarrow{F}\cdot \overrightarrow{dr}>0\Rightarrow Both\overrightarrow{F}and\overrightarrow{dr}areinthesamedirectionThereforebetweenEandFforceisrepulsive$