The potential energy of a particle is given by $U = A - Bx^2$,where $x$ is the displacement. What is the magnitude of the force acting on the particle?

When a stone is thrown vertically upwards and returns to the ground,at what point will its potential energy be maximum?

$A$ chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$). Calculate the work done to fold it as shown in diagram $(II)$.

Given in the figures are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case,specify the regions,if any,in which the particle cannot be found for the given energy. Also,indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

$A$ stretched rubber band has:

$A$ uniform chain of mass $M$ and length $L$ is lying on a smooth horizontal table,with half of its length hanging down. The work done in pulling the entire chain up onto the table is