$A$ force $F = (5\hat{i} + 3\hat{j}) \ N$ acts on an object,causing a displacement of $r = (2\hat{i} - 1\hat{j}) \ m$. Calculate the work done in $J$.

$A$ force of $(5\hat i + 6\hat j - 7\hat k) \, N$ is applied to a body of mass $10 \, kg$,causing it to displace from position $(4\hat i - 2\hat j + 5\hat k) \, m$ to $(8\hat i + 6\hat j - 3\hat k) \, m$. Calculate the work done in $J$.

$A$ body constrained to move along the $y$-axis is subjected to a constant force $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N}$. The work done by this force in moving the body a distance of $4 \text{ m}$ along the $y$-axis is ............... $J$.

$A$ particle of mass $m$ moves along a circular path of radius $r$ under the influence of a centripetal force $F$. What is the work done when the particle moves along a semi-circular path?

When a particle moves from its origin to a point with position vector $\vec{r} = (2\hat{i} - \hat{j}) \ m$,it is subjected to a force $\vec{F} = (5\hat{i} + 3\hat{j} + 2\hat{k}) \ N$. What is the work done by the force in Joules?

$A$ chain of mass $M$ and length $L$ is hanging from the edge of a table such that one-third of its length is hanging off the edge. The work done to pull the hanging part onto the table is: