$A$ particle is projected from a point at an angle $\theta$ with the horizontal direction. At any time $t$, if $p$ is the linear momentum, $y$ is the vertical displacement, and $x$ is the horizontal displacement, which of the following graphs does not represent the variation of kinetic energy $KE$ of the particle?

$A$ particle is projected with velocity $u$ from point $M$ on a frictionless incline of length $20\sqrt{2} \, m$. If it crosses a $40 \, m$ wide well at an angle of $45^o$,what should be its velocity at point $M$?

Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$,where $t$ is

Twelve persons are initially at $12$ corners of a regular polygon of $12$ sides of side length $a$. Each person moves with a uniform speed $v$ in such a manner that person $1$ is always directed towards person $2$,person $2$ towards person $3$,person $3$ towards person $4$,and so on. The time after which they meet is

$A$ car moving with a certain velocity jumps from an inclined plane placed at one bank of a river and reaches the other bank by attaining a maximum height of $80 \,m$. If the same car, moving with the same velocity, jumps from another inclined plane having a different angle of inclination and reaches the same point on the other bank by attaining a maximum height of $45 \,m$, then the width of the river is: (in $\,m$)

$A$ point mass $m$ is suspended from a light thread of length $l,$ fixed at $O,$ and is whirled in a horizontal circle at a constant speed as shown. From your point of view,stationary with respect to the mass,the forces acting on the mass are: