$A$ 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 action of force $\vec{F} = 4\hat{i} + \hat{j} + 3\hat{k} \text{ N}$. The work done will be ............ $\text{J}$.

$A$ force of $5 \ N$ is required to maintain a constant velocity of $2 \ m/s$ for a block of mass $10 \ kg$ on a rough surface. The work done by this force in $1 \ minute$ is: (in $J$)

Two constant forces ${F_1} = 2\hat i - 3\hat j + 3\hat k$ $(N)$ and ${F_2} = \hat i + \hat j - 2\hat k$ $(N)$ act on a body and displace it from the position ${r_1} = \hat i + 2\hat j - 2\hat k$ $(m)$ to the position ${r_2} = 7\hat i + 10\hat j + 5\hat k$ $(m)$. What is the work done in $J$?

$A$ body of mass $50 \ kg$ is lifted to a height of $20 \ m$ from the ground in two different ways as shown in the figure. The ratio of work done against gravity in both the respective cases will be:

If work is done by a body against a force,is the work considered positive or negative?

$A$ particle moves in the $x-y$ plane under the action of a force,$F = K \left[ \frac{x}{(x^2+y^2)^{3/2}} \hat{i} + \frac{y}{(x^2+y^2)^{3/2}} \hat{j} \right]$,where $K$ is a constant. The work done by the force when the particle moves from $(0, a)$ to $(a, 0)$ along a circular path of radius $a$ about the origin is: