An object of mass ' m ' initially at rest on a smooth horizontal plane starts moving under the action of force F =2 N. In the process of its linear…

An object of mass ' $\displaystyle m$ ' initially at rest on a smooth horizontal plane starts moving under the action of force $\displaystyle \mathrm{F}=2 \mathrm{~N}$. In the process of its linear motion, the angle $\displaystyle \theta$ (as shown in figure) between the direction of force and horizontal varies as $\displaystyle \theta=k x$, where k is a constant and $\displaystyle x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $\displaystyle E=\frac{n}{k} \sin \theta$. The value of n is $\displaystyle \_\_\_\_$.