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

$A$ particle is made to move from the origin in three spells of equal distances,first along the $x$-axis,second parallel to the $y$-axis,and third parallel to the $z$-axis. One of the forces acting on it has a constant magnitude of $50 \ N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal,and the total work done in all three spells is $300 \ J$. The final coordinates of the particle will be:

$A$ force $F = (5\hat{i} + 3\hat{j}) \ N$ acts on an object,causing a displacement of $r = (2\hat{i} - 1\hat{j}) \ m$. Calculate the work done in $J$.

$A$ small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action of force $5 \hat{i}+2 \hat{j}+7 \hat{k} \text{ N}$. The value of work done will be $............ \text{ J}$.

$A$ force $\overrightarrow{F} = 6\hat{i} + 2\hat{j} - 3\hat{k}$ acts on a particle and produces a displacement of $\overrightarrow{s} = 2\hat{i} - 3\hat{j} + x\hat{k}$. If the work done is zero,the value of $x$ is

At time $t=0$,a particle starts moving along the $x$-axis. If its kinetic energy increases uniformly with time $t$,the net force acting on it must be proportional to