$A$ 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?

$A$ chain of mass $m$ and length $\ell$ is held on a frictionless table in such a way that its $\frac{2 \ell}{5}$ part is hanging below the edge of the table. Find the work done to pull the hanging part of the chain up onto the table.

$A$ 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:

The figure shows three forces applied to a trunk that moves leftward by $3\, m$ over a smooth floor. The force magnitudes are $F_1 = 5\, N$,$F_2 = 9\, N$,and $F_3 = 3\, N$. The net work done on the trunk by the three forces is ............... $J$.

$A$ 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:

$A$ body of mass $5\, kg$ is placed at the origin and can move only on the $x$-axis. $A$ force of $10\, N$ is acting on it in a direction making an angle of $60^\circ$ with the $x$-axis and displaces it along the $x$-axis by $4\, m$. The work done by the force is $...\, J$.