$A$ $500\, kg$ crane takes a turn of radius $50\, m$ with a velocity of $36\, km/hr$. The centripetal force is ......... $N$.

$A$ car is moving on an overbridge of radius $R$ with a constant speed $v$. As the car is descending on the overbridge from point $B$ to $C$,the normal reaction on it due to the bridge:

$A$ 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 ......... $^o$ $(g = 9.8\, m/s^2)$.

$A$ particle describes a horizontal circle of radius $r$ in a conical funnel with a smooth inner surface with a speed of $v = 0.5 \text{ m/s}$. The height $h$ of the plane of the circle from the vertex of the funnel is (acceleration due to gravity, $g = 10 \text{ m/s}^2$): (in $\text{ cm}$)

$A$ rod $(AB)$ is attached to a fixed point $(C)$ using a light rope $(AC)$. The other end of the rod $(B)$ is resting on ice with negligible friction,and the system is in a stationary position. Which of the following can be the equilibrium configuration of this system?

$A$ mass $m$ is attached to one end of a spring with spring constant $k$ and natural length $l$. The system is rotated in a horizontal plane with an angular velocity $\omega$. What is the extension in the length of the spring?