$A$ body of mass $0.6 \, kg$ is moving along a circular path of radius $1 \, m$. If the body moves with $\frac{900}{\pi}$ revolutions per minute, its kinetic energy is: (in $ \, J$)

$A$ shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways,the product $t_1t_2$ is

In the figure shown,the two projectiles are fired simultaneously. The minimum distance between them during their flight is ........ $m$.

Two balls are thrown with the same velocity,one vertically upward and the other at an angle of $60^\circ$ with the vertical. What is the ratio of their potential energies at their respective maximum heights?

The position vector of a particle is given as $\vec{r} = (t^2 - 4t + 6)\hat{i} + (t^2)\hat{j}$. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to ....... $sec$.

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