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If a simple pendulum oscillates with an amplitude 50 mm and time period 2s, then its maximum velocity is
a)0.15 m/s
b)0.1 m/s
c)0.16 m/s
d)0.8 m/s
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If a simple pendulum oscillates with an amplitude 50 mm and time perio...
We know that in a simple harmonic motion the maximum velocity,
Vmax = A⍵
Here A = 50 mm
And ⍵ = 2π / T
= 2π / 2
= π
Hence  Vmax = 50 x 10-3.π
= 0.15 m/s
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Most Upvoted Answer
If a simple pendulum oscillates with an amplitude 50 mm and time perio...
Given data:
Amplitude, A = 50 mm = 0.05 m
Time period, T = 2 s

To find: Maximum velocity of the pendulum.

Formula: Maximum velocity of a simple pendulum = Aω
where,
A = Amplitude of oscillation
ω = Angular frequency = 2π/T

Calculation:
Angular frequency, ω = 2π/T = 2π/2 = π rad/s

Maximum velocity, v = Aω
v = 0.05 × π
v = 0.157 m/s

Rounding off to two significant figures, we get:
v ≈ 0.16 m/s

Therefore, the correct option is (b) 0.16 m/s.
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Ballistic pendulumThe ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. A Ballistic Pendulum is a device for measuring a bullet’s momentum and speed by employing perfectly inelastic collision. A large wooden block suspended by two cords serves as the pendulum bob. When a bullet is fired into the bob, it gets embedded in the bob and its momentum is transferred to the bob. The bullet’s momentum and velocity can be determined from the amplitude of the pendulum swing. The velocity of the bullet, in turn, can be derived from its calculated momentum.After collision, if the pendulum reaches a height h, then from principle of conservation of mechanical energywhere,m = mass of bulletM = mass of the bobvP = velocity of the bob-bullet combination∴ Now, Momentum before collision = Momentum after collisionwhere,vB = velocity of bullet∴ The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition (Nowadays, the ballistic pendulum. has now been replaced by the ballistic chronograph, an electronic devic e).The ballistic pendulum was invented by a

Ballistic pendulumThe ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. A Ballistic Pendulum is a device for measuring a bullet’s momentum and speed by employing perfectly inelastic collision. A large wooden block suspended by two cords serves as the pendulum bob. When a bullet is fired into the bob, it gets embedded in the bob and its momentum is transferred to the bob. The bullet’s momentum and velocity can be determined from the amplitude of the pendulum swing. The velocity of the bullet, in turn, can be derived from its calculated momentum.After collision, if the pendulum reaches a height h, then from principle of conservation of mechanical energywhere,m = mass of bulletM = mass of the bobvP = velocity of the bob-bullet combination∴ Now, Momentum before collision = Momentum after collisionwhere,vB = velocity of bullet∴ The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition (Nowadays, the ballistic pendulum. has now been replaced by the ballistic chronograph, an electronic devic e).In ballistic pendulum the collision is

Attempt All sub parts from each question.Galileo’s Isochronous Pendulum: Galileo observed a lamp swinging from ceiling at Pisa cathedral ceiling. He was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same. So, he concluded that the oscillations are isochronous. Anyhow, it was proved by advanced experimentation that the isochronism of simple pendulum is correct within 1% under the 30° of amplitude. It is confirmed that the period changes less than 1% until the amplitude is 30°. On the other hand, the period increased by more than 10% when the amplitude became larger than 80°. At the end of his life he devised a scheme for using a pendulum to regulate a mechanical clock. However, the first reliable pendulum clock was only demonstrated by Huygens 15 years after Galileo's death.Q. Who first observed the time period of a pendulum?

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If a simple pendulum oscillates with an amplitude 50 mm and time period 2s, then its maximum velocity isa)0.15 m/sb)0.1 m/sc)0.16 m/sd)0.8 m/sCorrect answer is option 'A'. Can you explain this answer?
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