$A$ force $F = (5\hat i + 3\hat j) \, N$ is applied to a particle,which displaces it from its origin to the point $r = (2\hat i - 1\hat j) \, m$. The work done on the particle is:

$A$ 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?

$A$ force $\vec{F}=(3 \hat{i}+4 \hat{j}) \;N$ acts on a particle moving in the $x-y$ plane. Starting from the origin,the particle first moves along the $x$-axis to the point $(4,0) \;m$ and then parallel to the $y$-axis to the point $(4,3) \;m$. The total work done by the force on the particle is ............. $J$.

When an object is dragged $10 \, m$ along a road,a frictional force of $200 \, N$ acts in the direction opposite to its motion. What is the work done by the frictional force on the object (in $, J$)?

If force and displacement of a particle in the direction of force are doubled,the work done would be:

$A$ force $\overrightarrow{F} = 6\hat{i} + 2\hat{j} - 3\hat{k}$ acts on a particle and produces a displacement of $\overrightarrow{s} = 2\hat{i} - 3\hat{j} + x\hat{k}$. If the work done is zero,the value of $x$ is