$A$ boy on a cycle pedals around a circle of $20\, m$ radius at a speed of $20\, m/s$. The combined mass of the boy and the cycle is $90\, kg$. The angle that the cycle makes with the vertical so that it may not fall is ......... $^o$ $(g = 9.8\, m/s^2)$.

When a vehicle of mass $m$ is moving with a velocity $v$ over a concave over-bridge of radius of curvature $r$,the thrust on the road at the lowest point on the bridge will be

$A$ 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 ...... $mm$ $(g = 10 \, m/s^2)$.

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

$A$ motorcycle is moving on an overbridge of radius $R$. The driver maintains a constant speed $v$. As the motorcycle is ascending on the overbridge,the normal force on it

$A$ train is moving towards north. At one place it turns towards north-east. Here,we observe that: