$A$ 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 $x$.

The figure shows a mass $m$ on a frictionless surface. It is connected to a rigid wall by means of a massless spring of spring constant $k$. Initially,the spring is at its natural position. If a force of constant magnitude $F$ starts acting on the block towards the right,then the speed of the block when the deformation in the spring is $x$ will be

$A$ force $\vec{F}=(3 \hat{i}+4 \hat{j}) \;N$ acts on a particle moving in the $x-y$ plane. Starting from the origin,the particle first moves along the $x$-axis to the point $(4,0) \;m$ and then parallel to the $y$-axis to the point $(4,3) \;m$. The total work done by the force on the particle is ............. $J$.

$A$ 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?

$A$ particle of mass $m$ is projected at an angle $\alpha$ to the horizontal with initial velocity $u \ m/s$. What is the work done by gravity during the time it reaches its highest point?

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