If at any point on the path of a projectile its velocity is $u$ at an inclination $\alpha$ to the horizontal,then after what time will it move at right angles to its former direction?

Choose the correct alternative$(s)$.

$A$ projectile is thrown at an angle $\theta$ to the horizontal from $O$ and it hits the ground at $O'$. During the entire motion (select the wrong statement):

$A$ point moves in the $xy$-plane according to the following equations: $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$, where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

Two bodies are projected from the ground with the same speed $40 \ m/s$ at two different angles with respect to the horizontal. The bodies were found to have the same range. If one of the bodies was projected at an angle of $60^{\circ}$ with the horizontal,then the sum of the maximum heights attained by the two projectiles is $....... \ m$. (Given $g = 10 \ m/s^2$)

Two stones of masses $m$ and $3m$ are whirled in horizontal circles, the heavier one in a radius $r/3$ and the lighter one in radius $r$. When both the stones experience same centripetal forces, the tangential speed of lighter stone is 'n' times that of the value of heavier stone. The value of 'n' is