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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Derive a formula for the length of second's pendulum.

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प्रश्न

Derive a formula for the length of second's pendulum.

थोडक्यात उत्तर
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उत्तर

∴ For second's pendulum,

`2 = 2pi sqrt("L"_"s"/"g")`

Where Ls is the length of seconds pendulum having period

T = 2s

∴ `"L"_"s" = "g"/"p"^2`

This is a formula for the length of second's pendulum.

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2021-2022 (March) Set 1

संबंधित प्रश्‍न

Answer in brief.

State the law of simple pendulum.


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.


What is a second pendulum?   


Obtain an expression for a time period of the simple pendulum.


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)


A bob of a simple pendulum has mass m and is oscillating with an amplitude a. If the length of the pendulum is L, then the maximum tension in the string is [cos 0° = 1, g = acceleration due to gravity]


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?


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 ______.


If a pendulum which gives correct time beats second on ground at a certain place is moved to the top of a tower 320 m high, then the loss of time of the pendulum clock in one day, in second, is ______.


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 pendulum performs S.H.M. with period `sqrt3` second in a stationary lift. If lift moves up with acceleration `"g"/3`, the period of pendulum is ______. (g = acceleration due to gravity)


Two simple pendulums of lengths 1.44 m and 1.96 m start swinging together. After how many vibrations will they again start swinging together?


The length of a seconds pendulum is 1m on the earth. If the mass and diameter of the planet is double than that of the earth, then the length of the second's pendulum on the planet will be ______ 


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)


The bob of a simple pendulum performs SHM with period T in air and with period T1 in water Relation between T and T1 is ______.

(neglect friction due to water, density of the material of the bob is = `9/8xx10^3` kgm3, density of water = 1 gcc-1) 


A pendulum bob is swinging in a vertical plane, such that its angular amplitude is less than 90°. At its highest point, the string is cut. Which trajectory is possible for bob afterwards?


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 ______.


The equation of motion in differential form for a seconds pendulum is ______.


A simple pendulum of length 196 cm performs linear SHM of amplitude 8 cm. Find the restoring force on its bob of mass 50 g at an extreme position.


At the highest point of its swing, a simple pendulum has maximum potential energy and minimum kinetic energy. What is the total mechanical energy of the pendulum at any point during its motion?


A simple pendulum is used to investigate the dissipation of energy. Which quantity is plotted against time to analyse this dissipation?


A student measures time for 20 oscillations of a simple pendulum as 30 s, 32 s, 35 s and 35 s. If the minimum division in the measuring clock is 1 s, then correct mean time (in second) is ______.


A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 90 cm. The period of oscillations of the sphere is ______. (g = 10 ms−2)


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