An aircraft executes a horizontal loop with a speed of $150\, m/s$ with its wings banked at an angle of $12^o$. The radius of the loop is ..........  $km$ $(g = 10\, m/s^2 \; and\; \tan 12^o = 0.2125)$

A particle comes round a circle of radius $1 \,m$ once. The time taken by it is $10 \,sec$. The average velocity of motion is

A particle starting from rest, moves in a circle of radius $r$. It attains a velocity of $\mathrm{V}_{0} \;\mathrm{m} / \mathrm{s}$ in the $\mathrm{n}^{\text {th }}$ round. Its angular acceleration will be

A small block slides down from rest at point $A$ on the surface of a smooth cylinder, as shown. At point $B$, the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by

A fly wheel is accelerated uniformly from rest and rotates through $5 \,rad$ in the first second. The angle rotated by the fly wheel in the next second, will be.........$rad$

A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero  ........ $rad/sec$