Circular Motion Questions

A bob of heavy mass $m$ is suspended by a light string of length $l$. The bob is given a horizontal velocity $v_0$ as shown in figure. If the string gets slack at some point $P$ making an angle $\theta$ from the horizontal, the ratio of the speed $v$ of the bob at point $P$ to its initial speed $v_0$ is:

The circular motion of a particle with constant speed is :

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone ?

A particle moves in a circle of radius $5\text{cm}$ with constant speed and time period $0.2\pi \text{s}$. The acceleration of the particle is:

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\text{m}$. The speed of the car at the top of the hill is between:

A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if:

A car of mass $m$ is moving on a level circular track of radius $R$. If ${\mu }_s$ is the static friction, the maximum speed is:

A car of mass $1000\text{kg}$ negotiates a banked curve of radius $90\text{m}$ on a frictionless road. If the banking angle is $45^{\circ }$, the speed of the car is:

Two stones of masses $m$ and $2m$ 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 the lighter stone is $n$ times that of the heavier stone when they experience same centripetal forces. The value of $n$ is:

A car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is ${\mu }_s$. The maximum safe velocity on this road is:

A particle moves so that its position vector is given by $\vec{r}=\cos \omega t\hat{x}+\sin \omega t\hat{y}$ where $\omega$ is a constant. Which of the following is true?

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop?

In the given figure, $a=15{\text{m/s}}^2$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2.5\text{m}$ at a given instant of time. The speed of the particle is: