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 $g = 10 \ ms^{-2}$)

$A$ car is moving with velocity $v$ at the top of a semi-circular hill of radius $40 \,m$ such that the normal force on it is zero. Find the velocity $(v)$ of the car. [Use $g=10 \,ms^{-2}$] (in $\,ms^{-1}$)

$A$ ball of mass $0.25 \,kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. What is the maximum speed with which the ball can be moved (in $\,m/s$)?

$A$ particle of mass $m$ is rotating in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on it is $F$. The relation between $F$,$L$,$r$,and $m$ is

$A$ mass of $0.5 \ kg$ is attached to a string moving in a horizontal circle with an angular velocity of $10 \ cycle/min$. Keeping the radius constant,the tension in the string is made $4$ times by increasing the angular velocity to $\omega$. The value of $\omega$ for that mass will be:

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