$A$ uniform chain of length $L = 2\,m$ is kept on a table such that a length $\ell = 60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $M = 4\,kg$. The work done in pulling the entire chain onto the table is ............. $J$. (Take $g = 10\,m/s^2$)

$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $u$. The force on the body is $mv^2/r$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

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

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 ...... .

$A$ force of $(4\hat i + \hat j + 3\hat k) \, N$ acts on a body,causing its displacement from $(3\hat i + 2\hat j - 6\hat k) \, m$ to $(14\hat i + 13\hat j + 9\hat k) \, m$. Calculate the work done in $J$.

$A$ 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 ........... $J$.