A string can bear a maximum tension of $31.6 \mathrm{N}$. What maximum number of revolutions per second can be made by a stone of mass $50 \mathrm{gm}$ tied to one end of a $1 \mathrm{m}$ long string so that the string may not break?

Find the maximum speed at which a car can turn round a curve of $30 \mathrm{m}$ radius on a level road if the coefficient of friction between that tyre and the road is $0.4$. Take $g=10 \mathrm{m}/{\mathrm{s}}^2$

A sphere of mass $200 \mathrm{gm}$ is attached to an inextensible string of length $130 \mathrm{cm}$ whose upper end is fixed to the ceiling. The sphere is made to describe circle of radius $50 \mathrm{cm}$. Calculate the time period of one revolution, and tension in the string.

A bucket full of water is tied with a rope $0.9 \mathrm{m}$ long and revolved in a vertical circle. What would be the minimum speed of the bucket at the highest point so that water may not fall. (Take $g=10 \mathrm{m}/{\mathrm{s}}^2$)

An electric bulb is suspended by a flexible wire from the ceiling of a train. The train goes horizontally round a curved path of radius $250 \mathrm{m}$. If the velocity of the train is $10 \mathrm{m}/\mathrm{s}$, find the angle the flexible wire makes with downward vertical. ($g=10 \mathrm{m}/{\mathrm{s}}^2$)

A stone is swung uniformly in a horizontal circle at the end of a thread $40 \mathrm{cm}$ long. At what number of revolutions per second, will the thread snap if it is known to do so under a load equal to eightfold weight of the stone? (Take $g=10 \mathrm{m}/{\mathrm{s}}^2$)

A pendulum has length $l$ and the mass of the bob is $m$. When it makes an angle $\alpha$ with the downward vertical, the velocity of the bob is $v$. Find the tension in the string at that instant.

The radius of curvature of a circular road is $r$ and its banking angle is $\theta$. Show that a car can negotiate the bend without skidding with a maximum velocity $v_{max}$ given by, $v_{max}={\left[\frac{r·g(\mu +\tan \theta )}{1-\mu \tan \theta }\right]}^{1/2}$ where $\mu$ is the coefficient of friction between the wheel of the car and the ground.