In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of $\omega$ . Which of them is correct graph between $T$ & $\omega .$

A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if 

Two stones of masses $m$ and $2\,m$ are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius $r.$ The tangential speed of lighter stone is $n$ times that of the value of heavier stone when they experience same centripetal forces. The value of $n$ is

A vehicle of mass $200\,kg$ is moving along a levelled curved road of radius $70\,m$ with angular velocity of $0.2\,rad / s$. The centripetal force acting on the vehicle is $.........\,N$

A car turns a corner on a slippery road at a constant speed of $10\,m/s$. If the coefficient of friction is $0.5$, the minimum radius of the arc in meter in which the car turns is

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu $, is