A child is sitting on a swing. Its minimum and maximum heights from the ground are 0.75 m and 2 m respectively. Its maximum speed will be
- A.10 m/s
- B.5 m/s
- C.8 m/s
- D.15 m/s
Correct answer
Explanation
The correct answer is B, 5 metres per second. A swing is a pendulum, and its speed is greatest at the lowest point, where all the potential energy gained at the top has turned into kinetic energy. The difference of height is two minus 0.75, that is 1.25 metres. By conservation of energy, half m v squared equals m g h, so v equals the square root of two g h, that is the square root of two times ten times 1.25, which is 5 metres per second. Option A is wrong because ten metres per second would need a height difference of five metres. Option C is wrong because eight metres per second corresponds to about 3.2 metres. Option D is wrong because fifteen metres per second is far too large for a swing of this size; it is simply the biggest number offered.
Read the full article: Oscillations: Simple Harmonic Motion and Pendulum Notes
Practice Questions
View allIf a particle is moving with simple harmonic motion, the velocity is _________ at the mean position.
- A.Maximum
- B.Zero
- C.Minimum
- D.None of these
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In simple harmonic motion the velocity is given by omega times the square root of A squared minus x squared.
Read the full explanation →The time period of a simple pendulum does not depend on which of the following?
- A.The length of the pendulum
- B.The mass of the bob
- C.The acceleration due to gravity
- D.All of these
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The time period of a simple pendulum is two pi times the square root of the length divided by g, in which the mass of the bob does not appear at all; a heavy bob and a light bob of the same length keep the same time, which is the…
Read the full explanation →The length of a second's pendulum, at a place where the acceleration due to gravity is 9.8 m/s squared, is nearly
- A.1 metre
- B.2 metres
- C.0.5 metre
- D.9.8 metres
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A second's pendulum is one whose time period is exactly two seconds, so that each swing from one side to the other takes one second.
Read the full explanation →If the length of a simple pendulum is made four times its original value, its time period will become
- A.Four times
- B.Two times
- C.Half
- D.One fourth
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The time period varies as the square root of the length, so multiplying the length by four multiplies the period by the square root of four, that is by two; to double the period of a pendulum its length must be made four times.
Read the full explanation →If a pendulum clock is taken from the earth to the moon, where the acceleration due to gravity is about one sixth, its time period will
- A.Decrease
- B.Increase
- C.Remain the same
- D.Become zero
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The time period varies inversely as the square root of g, so if g falls to one sixth, the period is multiplied by the square root of six, about 2.45 times; the pendulum swings more slowly and a pendulum clock taken to the moon would lose time badly.
Read the full explanation →