A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force $F$. if the centripetal force $F$ is kept constant but the angular velocity is doubled, the new radius of the path (original radius $R$ ) will be

A man standing on the roof of a house of height $h$ throws one particle vertically downwards and another particle horizontally with the same velocity $u$. The ratio of their velocities when they reach the earth's surface will be

A single wire $ACB$ passes through a smooth ring at $C$ which revolves at a constant speed in the horizontal circle of radius $r$ as shown in the figure. The speed of revolution is

Two particles each of mass $m$ are moving in horizontal circle with same angular speed. If both string are of same length then the ratio of tension in string $\frac{T_1}{T_2}$ is .........

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is

A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are $\vec{a}=2 \hat{i}+3 \hat{j} m / s ^2$ and $\overrightarrow{ p }=6 \hat{ i } + 4 \hat{ j } kgm /$ $s$. Then the motion of the particle is