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 $…..$

A vehicle of mass $m$ is moving on a rough horizontal road with momentum $P$. If the coefficient of friction between the tyres and the road be $\mu$, then the stopping distance is

A $4 \,kg$ mass and a $1\, kg$ mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

$A$ ball is projected vertically upwards. Air resistance  variation in $g$ may be neglected. The ball rises to its maximum height $H$ in a time $T$, the height being $h$ after a time $t$

$[1]$ The graph of kinetic energy $E_k$ of the ball against height $h$ is shown in figure $1$

$[2]$ The graph of height $h$ against time $t$ is shown in figure $2$

$[3]$ The graph of gravitational energy $E_g$ of the ball against height $h$ is shown in figure $3$

Which of $A, B, C, D, E$ shows the correct answers?

A bomb of $12 kg$ divides in two parts whose ratio of masses is $1 : 3$. If kinetic energy of smaller part is $216 J$, then momentum of bigger part in kg-m/sec will be