A particle moves in $x-y$ plane under the action of a force $\overrightarrow{F}=2A{x}^{2}y\hat{\mathrm{i}}+Ax{y}^2\hat{\mathrm{j}}$. Calculate the work done in going in an anticlockwise direction along the side of a square of vertices $\left(0, 0\right)$, $\left(1, 0\right)$, $\left(1, 1\right)$ and $\left(0, 1\right)$. Can this force be conservative?

A conservative force does $2 \mathrm{J}$ of work in moving a particle from $A$ to $C$ via $ABC$. The force does $-1 \mathrm{J}$ work when moving from $D$ to $F$, $3 \mathrm{J}$ for the path $EB$, $1 \mathrm{J}$ for $EF$ and $1 \mathrm{J}$ for $BC$. What is the work done by the force when the particle moves from $D$ to $C$?

A block is placed on the top of a plane inclined at $37°$ with horizontal. The length of the plane is $5 \mathrm{m}$. The block slides down the plane and reaches the bottom.

$\left(\mathrm{a}\right)$ Find the speed of the block at the bottom, if the inclined plane is smooth.
$\left(\mathrm{b}\right)$ Find the speed of the block at the bottom, if the coefficient of friction is $0.25$.

A smooth block of mass $m$ is released from rest from a height $h$. It slides and compresses the spring of stiffness $k$. Find the maximum compression of the spring. Taking block spring a system. No external force is doing work on the system and no non-conservative force is present. The mechanical energy should be conserved. $\mathrm{\Delta }K+\mathrm{\Delta }U=0$

A block of mass $m$ is suddenly released from the top of a spring of stiffness constant $k$.

$\left(\mathrm{a}\right)$ Find the acceleration of the block just after release.
$\left(\mathrm{b}\right)$ What is the compression in the spring at equilibrium.
$\left(\mathrm{c}\right)$ What is the maximum compression in the spring.
$\left(\mathrm{d}\right)$ Find the acceleration of the block at maximum compression in the spring.

A block of mass $m$ strikes a light pan fitted with a vertical spring after falling through a distance $h$. If the stiffness of the spring is $k$, find the maximum compression of the spring.

A chain of length $L$ and mass $M$ is held on a frictionless table with $\left(\frac{1}{n}\right)$^th of its length hanging over the edge. When the chain is released, find the velocity of chain while leaving the table.

A body of mass $m$ hangs by an inextensible string that passes over a smooth mass less pulley that is fitted with a light spring of stiffness $k$ as shown in figure. If the body is released from rest and the spring is undeformed, calculate the maximum elongation of the spring.