$A$ 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?

$A$ chain of mass $4 \ kg$ and length $2 \ m$ is hanging such that one-fourth of its length is hanging over the edge of a table. The work done to pull the hanging part onto the table is . . . . . . $J$. (Take $g = 10 \ m/s^2$)

$A$ body of mass $2 \ kg$ is moving along the $x$-direction such that its displacement as a function of time is given by $x(t) = \alpha t^2 + \beta t + \gamma \ m$, where $\alpha = 1 \ m/s^2$, $\beta = 1 \ m/s$, and $\gamma = 1 \ m$. The work done on the body during the time interval $t = 2 \ s$ to $t = 3 \ s$ is . . . . . . $J$.

$A$ ship of mass $3 \times 10^7 \, kg$ initially at rest is pulled by a force of $5 \times 10^4 \, N$ through a distance of $3 \, m$. Assuming that the resistance due to water is negligible,the speed of the ship is ........... $m/s$.

$A$ body constrained to move along the $z$-axis of a coordinate system is subject to a constant force $F$ given by $F = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ N}$,where $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along the $x, y,$ and $z$-axes of the system respectively. What is the work done (in $J$) by this force in moving the body a distance of $4 \text{ m}$ along the $z$-axis?

$A$ particle is displaced from point $P(3 \ m, 4 \ m, 5 \ m)$ to a point $Q(2 \ m, 3 \ m, 4 \ m)$ under a constant force $\vec{F}=(3 \hat{i}+4 \hat{j}+5 \hat{k}) \ N$. The work done by the force in this process is