$A$ cyclist goes round a circular path of circumference $34.3 \ m$ in $\sqrt{22} \ s$. The angle made by him with the vertical will be ....... $^o$.

$A$ body of mass $5\, kg$ is moving in a circle of radius $1\, m$ with an angular velocity of $2\, rad/s$. The centripetal force is ......... $N$.

$A$ string of length $L$ fixed at one end carries a mass $m$ at the other end. The string makes $3/\pi$ r.p.s. around the vertical axis through the fixed end. The tension in the string is: (in $mL$)

When a disc is rotating with angular velocity $\omega$,a particle situated at a distance of $4 \ cm$ just begins to slip. If the angular velocity is doubled,at what distance will the particle start to slip (in $cm$)?

$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

An aircraft executes a horizontal loop of radius $9 \ km$ at a constant speed of $540 \ kmh^{-1}$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $g = 10 \ ms^{-2}$)