$A$ body of mass $m$ kg is lifted by a man to a height of one metre in $30\, s$. Another man lifts the same mass to the same height in $60\, s$. The work done by them are in the ratio:

$A$ string is used to pull a block of mass $m$ vertically up by a distance $h$ at a constant acceleration $\frac{g}{4}$. The work done by the tension in the string is ...............

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 ...... .

Define work exerted by force.

$A$ 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 $1\,kg/litre$.)

$A$ 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 $J$.