Advertisements
Advertisements
प्रश्न
A simple pendulum performs S.H.M. of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one-third of its amplitude.
Advertisements
उत्तर
Data: T= 4 s, x = A/3
The displacement of a particle starting into SHM from the mean position is x = A sin wt = A sin `(2π)/"T"`t
∴ A sin `(2π)/"T"`t = `"A"/3`
∴ `(2π)/"T"`t = sin-1 0.3333 = 19.47° = `19.47xxπ/180`rad
∴ `2/4`t = `19.47/180`
∴ t = `19.47/90` = 0.2163 s
∴ The displacement of the bob will be one-third of its amplitude 0.2163 s after crossing the mean position.
APPEARS IN
संबंधित प्रश्न
A simple pendulum of length 100 cm performs S.H.M. Find the restoring force acting on its bob of mass 50 g when the displacement from the mean position is 3 cm.
In a second’s pendulum, the mass of Bob is 50 g. If it is replaced by 100 g mass, then its period will be ______.
What is a second pendulum?
Obtain an expression for a time period of the simple pendulum.
A simple pendulum of length L has mass m and it oscillates freely with amplitude A. At the extreme position, its potential energy is (g = acceleration due to gravity)
A simple pendulum of length I has a bob of mass m. It executes SHM of small amplitude A. The maximum tension in the string is (g = acceleration due to gravity)
The length of a simple pendulum is increased by 44%. The percentage change in its time period is ______.
Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross-section, by 1 mm?
A simple pendulum has a time period T1 when on the earth's surface and T2 when taken to a height R above the earth's surface, where R is the radius of the earth. The value of T2 / T1 is ______.
Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulums is ______.
Two light balls are suspended as shown in figure. When a stream of air passes through the space between them, the distance between the balls will ______.
A person measures a time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration `("g"/3)`, the time period of the pendulum will be ______.
A simple pendulum has length 'L1'. When its amplitude is 'a' cm, its energy is 'E1'. When length is 2L1, its energy is 'E2' Amplitude is same for both the lengths The relation between E1 and E2 is ______.
A simple pendulum has a length of 2m and a bob of mass of 100 grams. It is whirled in a horizontal plane. If the string breaks under a tension of 10 N, the angle made by the string with vertical is ______
(g = 10 m/s2)
The maximum kinetic energy of a simple pendulum is 'K'. Its displacement in terms of amplitude 'a', when kinetic energy becomes `(K/2)` is ______.
The maximum frequency of transmitted radio waves above which the radio waves are no longer reflected back by ionosphere is ______.
(N = maximum electron density of lonosphere, g = acceleration due to gravity)
Two weights w1 and w2 are suspended from the ends of light string over a smooth fixed pulley. If the pulley is pulled up with acceleration g, the tension in the string will be ______.
A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10°C and coefficient of linear expansion of the metal of the rod is 2 × 106 °C-1, the period of pendulum will increased by ______.
A clock regulated by a second pendulum keeps the correct time. During winter the length of the pendulum decreases by 1 %. How much will the clock gain or lose in one day?
The velocity of bob of a second’s pendulum when it is 6 cm from its mean position and amplitude of 10 cm, is ______.
A simple pendulum is used to investigate the dissipation of energy. Which quantity is plotted against time to analyse this dissipation?
