$A$ particle performs uniform circular motion in a horizontal plane. The radius of the circle is $20 \, cm$. The centripetal force acting on the particle is $10 \, N$. Its kinetic energy is ........ $J$.

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

$A$ stone of mass $m$ is tied to a string of length $l$ and rotated in a circle with a constant speed $v$. If the string is released,the stone flies:

$A$ particle is projected from the ground with an initial speed $v$ at an angle $\theta$ with the horizontal. The average velocity of the particle between its point of projection and the highest point of its trajectory is

Two particles $A$ and $B$ are projected simultaneously in the directions shown in the figure with velocities $V_A = 20 \ ms^{-1}$ and $V_B = 10 \ ms^{-1}$ respectively. They collide in the air after $0.5 \ s$. Find $(a)$ the angle $\theta$ and $(b)$ the distance $x$.

$A$ projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal with a velocity of $140 \,ms^{-1}$. Then the time after which its velocity makes an angle $45^{\circ}$ with the horizontal is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,s$)