$A$ 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 $\,m/s$)?

$A$ 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:

As shown in the figure,two strings of length $l$ each are attached to a vertical axis $AB$ of length $l$. The strings are $AC$ and $BC$. At point $C$,a point mass $m$ is attached. The mass rotates about the axis with angular velocity $\omega$. The tensions in strings $AC$ and $BC$ are $T_1$ and $T_2$ respectively. Choose the $CORRECT$ alternative:

$A$ particle moves in a horizontal circle on the smooth inner surface of a hemispherical bowl of radius $R$. The plane of motion is at a depth $d$ below the centre of the hemisphere. The speed of the particle is:

$A$ ball of mass $m$ is attached to the free end of an inextensible string of length $\ell$. Let $T$ be the tension in the string. The ball is moving in a horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be

$A$ particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of the plane of the circle above the vertex is $h$. The speed of the particle should be