An aircraft executes a horizontal loop at a speed of $720 \; km/h$ with its wings banked at $15^{\circ}$. What is the radius of the loop in $km$?

$A$ bob of mass $m$ is whirled in a horizontal plane by means of a string of length $\ell$ with an initial angular speed of $\omega$. The tension in the string is $T$. If the angular speed becomes $2\omega$ while keeping the same radius $\ell$,the tension in the string becomes:

$A$ 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 ......... $N$.

In a conical pendulum,the bob of mass $m$ moves in a horizontal circle of radius $r$ with uniform speed $V$. The string of length $L$ describes a cone of semi-vertical angle $\theta$. The centripetal force acting on the bob is $(g = \text{acceleration due to gravity})$

Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta$ with respect to each other. They are connected by a spring with spring constant $k$. The angular frequency of small oscillations for the motion where the two masses always stay at the same distance from the meeting point of the rails is:

$A$ particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R^{3}$. Its time period of revolution will be given by