$A$ car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud,as they leave the ground,are thrown:

$A$ body of mass '$m$' is projected with a speed '$u$' making an angle of $45^{\circ}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt{2} mu^3}{Xg}$. The value of '$X$' is

The range of a projectile of mass $1\, kg$ is $80\, m$ while it attains a maximum height of $20\, m$. Its change in momentum during the complete motion is ............ $N-s$.

$A$ point $P$ on the circumference of a wheel is initially in contact with the ground. If the radius of the wheel is $5 \, m$,what will be the displacement of point $P$ when the wheel rolls forward by half a revolution?

$A$ particle is projected from the ground with velocity $u$ at an angle $\theta$ from the horizontal. Match the following two columns.

Column $I$	Column $II$
$(A)$ Average velocity between initial and final points	$(p)$ $u \sin \theta$
$(B)$ Change in velocity between initial and final points	$(q)$ $u \cos \theta$
$(C)$ Change in velocity between initial and highest points	$(r)$ Zero
$(D)$ Average velocity between initial and highest points	$(s)$ None of the above

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown in the figure. The time of flight $T$ is given by ........ $\text{s}$.