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?

$A$ 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 $J$)

$A$ horizontal force of $10 \ N$ is applied on a block of mass $1.5 \ kg$ which is initially at rest on a rough horizontal surface. The work done by the applied force in a time of $6 \ s$ from the beginning of the motion is (Acceleration due to gravity $= 10 \ m/s^2$; the coefficient of kinetic friction between the block and the surface is $0.2$). (in $J$)

$A$ force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\vec{S} = \hat{i} - 2\hat{j} - \hat{k}$. What will be the value of $b$,if the work done on the particle is zero?

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

$A$ man of mass $50 \ kg$ carries a load of mass $20 \ kg$ and climbs $20$ steps,each of height $0.25 \ m$. Calculate the work done in $J$.