$A$ force $\vec F = 3\hat i + c\hat j + 2\hat k$ acting on a particle causes a displacement $\vec S = - 4\hat i + 2\hat j - 3\hat k$. If the work done is $6 \ J$,then the value of $c$ will be:

$A$ body is being raised to height $h$ from the surface of the Earth. What is the sign of work done by $(a)$ applied force and $(b)$ gravitational force?

$A$ particle of mass $100 \ g$ is projected vertically upwards with a speed of $5 \ m/s$. What is the work done by the force of gravity during the time the particle returns to the starting point? (in $J$)

$A$ weightlifter lifts a weight off the ground and holds it up.

$A$ uniform rope of length $4 \,m$ and mass $0.4 \,kg$ is held on a frictionless table in such a way that $0.6 \,m$ of the rope is hanging over the edge. The work done to pull the hanging part of the rope onto the table is, (Assume $g = 10 \,m/s^2$) (in $\,J$)

If a force $(3 \hat{i} + 2 \hat{j} + 5 \hat{k}) \text{ N}$ acting on a body displaces it through $(2 \hat{i} + 2 \hat{j} + 1 \hat{k}) \text{ m}$,then the work done by the force on the body is (in $J$)