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 motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta= kx$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E =\frac{ n }{ k } \sin \theta$. The value of $n$ is $.....$

Masses of two substances are $1\, g$ and $9\, g$ respectively. If their kinetic energies are same, then the ratio of their momentum will be

The graph between $E$ and $v$ is

A point particle of mass $0.5 \,kg$ is moving along the $X$-axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$. What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

If the K.E. of a particle is doubled, then its momentum will

The slope of kinetic energy displacement curve of a particle in motion is