$A$ 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 $(II)$.

The decrease in the potential energy of a ball of mass $20 \,kg$ which falls from a height of $50 \,cm$ is ............ $J$.

The potential energy of a particle is given by $U = 8x^2 - 4x + 400 \, J$. Find the position $x$ where the force acting on the particle is zero.

$A$ uniform chain of length $l$ and mass $m$ lies on the surface of a smooth hemisphere of radius $R$ $(R > l)$ with one end tied to the top of the hemisphere as shown in the figure. Gravitational potential energy of the chain with respect to the base of the hemisphere is

The work done in moving a body of mass $2 \,kg$ to a height of $4 \,m$ from the surface of the earth is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,J$)

$A$ particle is placed at the origin and a force $F = kx$ is acting on it (where $k$ is a positive constant). If $U(0) = 0$,the graph of $U(x)$ versus $x$ will be (where $U$ is the potential energy function):