Two bodies of masses $m$ and $3m$ are rotating in horizontal circles of radii $r$ and $\frac{r}{3}$ respectively. The tangential speed of the body of mass $m$ is $n$ times that of the heavier body. If the centripetal force is the same for both,the value of $n$ is:

In dealing with the motion of a projectile in the air,we ignore the effect of air resistance on the motion. This gives a trajectory that is a parabola,as you have studied. What would the trajectory look like if air resistance is included? Sketch such a trajectory and explain why you have drawn it that way.

An aircraft is flying at a height of $H$ above the ground at a constant speed $V$. What is the maximum angle subtended at a ground observation point by the aircraft's path after time $T$?

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

$A$ projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

$A$ 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: