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

$A$ 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:

$A$ 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

$A$ ball of mass $m$ is attached to a string whose other end is fixed. The system is free to rotate in a vertical plane. When the ball swings,no work is done on the ball by the tension in the string. Which of the following statements is the correct explanation?

Calculate the work done by a car against gravity in moving along a straight horizontal road. The mass of the car is $400\,kg$ and the distance moved is $2\,m$. (in $,J$)