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 $25 \,N$. ..........  $m/s$ is the maximum speed with which the ball can be moved

Defined optimum speed.

A car is moving on a circular level road of curvature $300\,metres.$ If the coefficient of friction is $0.3$ and acceleration due to gravity is $10\,m/s^2,$ the maximum speed the car can have is ........ $km/hr$ 

A cyclist is travelling with velocity $v$ on a curved road of radius $R$. The angle $\theta$  through which the cyclist leans inwards is given by

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

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