Two balls are thrown simultaneously from the ground with the same velocity of $10\,m/s$ but at different angles of projection with the horizontal. Both balls fall at the same distance $5\sqrt{3}\,m$ from the point of projection. What is the time interval between the balls striking the ground?

$A$ car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take the same time to complete the circles,the ratio of their angular speeds and linear speeds will be .........

Two particles are projected from a tower in opposite directions horizontally with speed $10\,m/s$ each. At $t=1\,s$,match the following two columns.

Column $I$	Column $II$
$(A)$ Relative acceleration between two	$(p)$ $0$ $SI$ unit
$(B)$ Relative velocity between two	$(q)$ $5$ $SI$ unit
$(C)$ Horizontal distance between two	$(r)$ $10$ $SI$ unit
$(D)$ Vertical distance between two	$(s)$ $20$ $SI$ unit

As shown in the figure,there is a spring-block system. $A$ block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring by $5.0\,cm$. The spring constant is $500\,N/m$. When released,calculate the horizontal distance from the edge of the table where it will hit the ground $4\,m$ below the spring. $(g = 10\,m/s^2)$

An aircraft executes a horizontal loop with a speed of $150\, m/s$ with its wings banked at an angle of $12^\circ$. The radius of the loop is .......... $km$ $(g = 10\, m/s^2 \text{ and } \tan 12^\circ = 0.2125)$

$A$ stone thrown with velocity $u$ at angles $\theta$ and $(90^{\circ}-\theta)$ with the horizontal reaches maximum heights $H_1$ and $H_2$ respectively. Its horizontal range is