$A$ 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 $J$)

$A$ particle moves from position $\vec{r_1} = 3\,\hat{i} + 2\,\hat{j} - 6\,\hat{k}$ to position $\vec{r_2} = 14\,\hat{i} + 13\,\hat{j} + 9\,\hat{k}$ under the influence of a force $\vec{F} = 4\,\hat{i} + \hat{j} + 3\,\hat{k}$. Find the work done in $J$.

$A$ heavy box of $40\, kg$ is pushed along $20\, m$ by two coolies over a railway platform whose coefficient of friction with the box is $0.4$. The work done by the two coolies is: .................. $J$ (Take $g = 10\, m/s^2$)

$A$ man carries a bucket of weight $60 \ N$ and walks $7 \ m$ in the horizontal direction,then climbs $5 \ m$ in the vertical direction. What is the work done by the man in $J$?

$A$ ball of mass $m$ is attached to a string whose other end is fixed. The system is free to rotate in a vertical plane. When the ball swings,no work is done on the ball by the tension in the string. Which of the following statements is the correct explanation?

When a particle moves from its origin to a point with position vector $\vec{r} = (2\hat{i} - \hat{j}) \ m$,it is subjected to a force $\vec{F} = (5\hat{i} + 3\hat{j} + 2\hat{k}) \ N$. What is the work done by the force in Joules?