$A$ ball of mass $100 \ g$ is projected with velocity $20 \ m/s$ at $60^{\circ}$ with the horizontal. The decrease in kinetic energy of the ball during the motion from the point of projection to the highest point is:

$A$ 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

Two bodies of mass $10 \ kg$ and $5 \ kg$ are moving in concentric circular orbits of radii $R$ and $r$ respectively such that their periods are same. The ratio between their centripetal acceleration is

$A$ particle is projected from the horizontal making an angle of $53^{\circ}$ with an initial velocity of $100\,m/s$. The time taken by the particle to make an angle of $45^{\circ}$ with the horizontal is $.........\,s$.

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$,where $\alpha$ and $\beta$ are constants. The speed of the particle at time $t$ is given by:

At a given instant of time,two particles have position vectors $4 \hat{i} + 4 \hat{j} + 57 \hat{k} \ m$ and $2 \hat{i} + 2 \hat{j} + 5 \hat{k} \ m$ respectively. If the velocity of the first particle is $0.4 \hat{i} \ ms^{-1}$,what is the velocity of the second particle in $ms^{-1}$ if they collide after $10 \ s$?