$A$ metal chain of mass $2 \,kg$ and length $90 \,cm$ hangs over a table with $60 \,cm$ on the table. How much work needs to be done to pull the hanging part of the chain back onto the table (in $\,J$)? (Let $g=10 \,m/s^2$)

Calculate the work done by pump $P$ to transfer water of density $d$ from one container to another as shown in the figure.

$A$ particle with constant total energy $E$ moves in one dimension in a region where the potential energy is $U(x)$. The speed of the particle is zero where

For the stability of a physical system,what should be its potential energy? Should it be more or less?

$A$ point particle of mass $0.5 \,kg$ is moving along the $X$-axis under a force described by the potential energy $V$ shown in the graph. It is projected towards the right from the origin with a speed $v$. What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

$A$ 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