$A$ force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle, causing a displacement $\vec{S} = \hat{i} - 2\hat{j} - \hat{k}$. If the work done on the particle is zero, what is the value of $b$?

If a person is pushing a box inside a moving train,the work done in the frame of the earth will be: (where $\vec{s}$ is the displacement of the box in the train and $\vec{s}_0$ is the displacement of the train relative to the ground)

$A$ force $\vec{F} = 6\hat{i} + 2\hat{j} - 3\hat{k}$ acts on a particle,causing a displacement $\vec{S} = 2\hat{i} - 3\hat{j} + x\hat{k}$. If the work done during this displacement is zero,find the value of $x$.

$A$ sphere of mass $m$ is tied to one end of a string of length $l$ and rotated through the other end along a horizontal circular path with speed $v$. The work done in a full horizontal circle is

In the figure shown,all the surfaces are frictionless,and the mass of the block $m$ is $1\,kg$. The block and wedge are held initially at rest. Now,the wedge is given a horizontal acceleration of $5\,m/s^2$ by applying a force on the wedge,such that the block does not slip on the wedge. Then,the work done by the normal force in the ground frame on the block in $2\,sec$ is ............... $J$.

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 $J$?