$A$ 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

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:

$A$ ball of mass $m = 0.5 \ kg$ is attached to the end of a string having length $L = 0.5 \ m$. The ball is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is $324 \ N$. The maximum possible value of angular velocity of the ball (in $rad/s$) is

The $x$ and $y$ displacements of a particle are given as $x(t) = a \sin \omega t$ and $y(t) = a \sin 2 \omega t$. Its trajectory will look like:

$A$ string of length $L$ fixed at one end carries a body of mass $m$ at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes an angle $\theta$ with the vertical. The angular frequency of the body is $\omega$. The tension in the string is

$A$ stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string? (Length of stick is same in all scenarios)