$A$ force $\vec{F} = -5 \hat{i} - 7 \hat{j} + 3 \hat{k}$ acting on a particle causes a displacement $\vec{s} = 3 \hat{i} - 2 \hat{j} + a \hat{k}$. If the work done is $14 \ J$,then the value of '$a$' is:

Two constant forces ${F_1} = 2\hat i - 3\hat j + 3\hat k$ $(N)$ and ${F_2} = \hat i + \hat j - 2\hat k$ $(N)$ act on a body and displace it from the position ${r_1} = \hat i + 2\hat j - 2\hat k$ $(m)$ to the position ${r_2} = 7\hat i + 10\hat j + 5\hat k$ $(m)$. What is the work done in $J$?

$A$ block of mass $m$ is pulled along a circular arc by means of a constant horizontal force $F$ as shown. Work done by this force in pulling the block from $A$ to $B$ is ............

$A$ 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?

If a person is pushing a box inside a moving train,the work done in the frame of the earth will be: (where $\vec{s}$ is the displacement of the box in the train and $\vec{s}_0$ is the displacement of the train relative to the ground)

$A$ 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: