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प्रश्न
Answer in brief.
State the law of simple pendulum.
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उत्तर
At a given place, the period of a simple pendulum is
T = 2π `sqrt("L"/"g")`
where,
L - length of the simple pendulum,
g - is the acceleration due to gravity at that place.
From the above expression, the laws of a simple pendulum are as follows:
- Law of length: The period of a simple pendulum at a given place (g constant) is directly proportional to the square root of its length.
- Law of acceleration due to gravity: The period of a simple pendulum of a given length (L constant) is inversely proportional to the square root of the acceleration due to gravity.
- Law of mass: The period of a simple pendulum does not depend on the mass.
- Law of isochronism: The period of a simple pendulum does not depend on its amplitude (for small amplitude).
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संबंधित प्रश्न
Define an ideal 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.
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.
What is a second pendulum?
Obtain an expression for a time period of the simple pendulum.
The length of a simple pendulum is increased by 44%. The percentage change in its time period is ______.
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?
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 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 ______.
The period of simple pendulum is measured as T in a stationary lift. If the lift moves upward with an acceleration of 5 g, the period 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 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 maximum kinetic energy of a simple pendulum is 'K'. Its displacement in terms of amplitude 'a', when kinetic energy becomes `(K/2)` is ______.
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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 ______.
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.
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?
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)
