$A$ body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of $30^\circ$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$.

If two stones are projected at angles $\theta$ and $(90^{\circ}-\theta)$ respectively with the horizontal with a speed of $20 \ ms^{-1}$. If the second stone rises $10 \ m$ higher than the first stone,then the angle of projection $\theta$ is (acceleration due to gravity $g = 10 \ ms^{-2}$) (in $^{\circ}$)

Assertion: In a circular motion,work done by centripetal force is not always zero.
Reason: If the speed of the particle increases or decreases in circular motion,then the net force acting on the particle does not remain towards the centre.

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

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 $x$.

$A$ 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 .........