$A$ string breaks if its tension exceeds $10 \, N$. $A$ stone of mass $250 \, g$ tied to this string of length $10 \, cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$.

$A$ 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:

$A$ 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

"Momentum and changes in momentum are not always in the same direction." Explain with a suitable example.

$A$ single wire $ACB$ passes through a smooth ring at $C$ which revolves at a constant speed in a horizontal circle of radius $r$ as shown in the figure. The speed of revolution is

$A$ conical pendulum is moving in a circle with angular velocity $\omega$ as shown. If the tension in the string is $T$,which of the following equations is correct?