The centripetal acceleration of a particle in uniform circular motion is $18 \,m/s^2$. If the radius of the circular path is $50 \,cm$, the change in velocity of the particle in a time of $\frac{\pi}{18} \,s$ is (in $\,m/s$)

$A$ ball of mass $m$ is thrown vertically upward. Another ball of mass $2m$ is thrown at an angle $\theta$ with the vertical. Both the balls stay in the air for the same period of time. The ratio of the maximum heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is $.....$

The position vector of a particle is given as $\vec{r} = (t^2 - 8t + 12)\hat{i} + t^2\hat{j}$. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to ........ $sec$.

The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it will be:

An athlete completes one round of a circular track of radius $10 \, m$ in $40 \, sec$. The distance covered by him in $2 \, min \ 20 \, sec$ is ........ $m$.

$A$ ball is rolled off along the edge of a horizontal table with velocity $4 \, m/s$. It hits the ground after time $0.4 \, s$. Which of the following are correct?