Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ respectively from the horizontal,then the trajectory of particle $1$ with respect to particle $2$ will be:

$A$ stone of mass $0.25 \; kg$ is tied to the end of a string and is being whirled in a horizontal circle of radius $1.5 \; m$ with a speed of $40 \; rev./min$. If the speed of the stone is increased beyond the maximum permissible value and the string breaks suddenly,which of the following correctly describes the trajectory of the stone after the string breaks?
$(a)$ The stone moves radially outward.
$(b)$ The stone flies off tangentially from the instant the string breaks.
$(c)$ The stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle.

Four particles $A, B, C$ and $D$ are moving with constant speed $v$ each. At the instant shown,the relative velocities of $A$ with respect to $B, C$ and $D$ are in the directions:

When a body moves with a constant speed along a circle,

Three particles start simultaneously from a point on a horizontal smooth plane. The first particle moves with speed $v_1$ towards the east,the second particle moves towards the north with speed $v_2$,and the third one moves towards the north-east. The velocity of the third particle,such that the three particles always lie on a straight line,is

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