Vertical Circle: Speed & Tension

A stone of mass m is tied to a string and is moved in a vertical circle of radius r making 'n' r.p.m. The total tension in the string when the stone is at the lowest point is ($g$ = acceleration due to gravity)

A stone of mass $40$ g is tied to a light inextensible string of length $50$ cm and whirled in a vertical circle at the rate of $30$ revolutions per minute. The tension in the string when it is at the lowest point of the circle is

(Take gravitational acceleration, $g = 10$ m/s$^{2}$ and $\pi^2 = 10$)

The maximum and minimum tensions in the string whirling in a circle of radius $2.5$ m are in the ratio $5 : 3$ then its velocity is ($g = 10$ m/s$^{2}$)

A simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is twice the minimum tension then $\theta$ is

A stone of mass ' m ' kg is tied to a string of length ' $L$ ' $m$ and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take $\pi^2 = 10$ and acceleration due to gravity, $g = 10\text{ m/s}^2$ ]

A pendulum bob has a speed $4\text{ m/s}$ at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of $60^\circ$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $g = 10\text{ m/s}^2, \cos 60^\circ = 0.5$)

A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, $g = 10\text{ m/s}^2$)

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point $A$ is $10\text{ m/s}$. The ratio of its kinetic energies at point B and C is:

(Take acceleration due to gravity as $10\text{ m/s}^2$)

A simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is 4 times the minimum tension then the value of $\theta$ is

A stone of mass $900\text{ g}$ is tied to a string and moved in a vertical circle of radius $1\text{ m}$ making $10\text{ rpm}$. The tension in the string, when the stone is at the lowest point is (if $\pi^2 = 9.8$ and $g = 9.8\text{ m/s}^2$):

The string of pendulum of length ' $L$ ' is displaced through $90^\circ$ from the vertical and released. Then the maximum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is ( $m =$ mass of pendulum, $g =$ acceleration due to gravity)

A simple pendulum of length $2\text{ m}$ is given a horizontal push through angular displacement of $60^\circ$. If the mass of bob is 200 gram, the angular velocity of the bob will be (Take Acceleration due to gravity $= 10\text{ m/s}^2$) $\left(\sin 30^\circ = \cos 60^\circ = 0.5, \cos 30^\circ = \sin 60^\circ = \sqrt{3}/2\right)$

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{2(u^2 - gL)}$. The value of x is -

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5: 1. The velocity of the bob at the highest position is ________ m/s. (Take g = 10 m/s2)

A stone of mass 1 kg is tied to a string 2 m long and it's rotated at constant speed of $40\text{ m s}^{-1}$ in a vertical circle. The ratio of the tension at the top and the bottom is [Take $g = 10\text{ m s}^{-2}$ ]