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

$A$ person draws water from a $5\,m$ deep well using a bucket of mass $2\,kg$ and capacity $8\,litre$ with a rope of mass $1\,kg.$ What is the total work done by the person? (Assume $g = 10\,m/s^2$ and the density of water is $1\,kg/litre$.)

How much work does a pulling force of $40\, N$ do on a $20\, kg$ box in pulling it $8\, m$ across a smooth floor at a constant speed? The pulling force is directed at $60^{\circ}$ above the horizontal. (Answer in $J$)

Two persons $A$ and $B$ perform the same amount of work in moving a body through a certain distance $d$ with the application of forces acting at angles $45^{\circ}$ and $60^{\circ}$ with the direction of displacement,respectively. The ratio of the force applied by person $A$ to the force applied by person $B$ is $\frac{1}{\sqrt{x}}$. The value of $x$ is ...... .

The work done in moving an object from the origin to a point whose position vector is $\vec{r} = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $\vec{F} = 2 \hat{i} - \hat{j} - \hat{k}$ is:

$A$ porter lifts a heavy suitcase of mass $80\, \text{kg}$ and at the destination lowers it down by a distance of $80\, \text{cm}$ with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (Take $g = 9.8\, \text{m/s}^2$) (In $\text{J}$)