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A simple pendulum of length 5 m, with a bob of mass 1 kg, is in simple harmonic motion as it passes through its mean position, the bob has a speed of 5 m/s. The net force on the bob at the mean position is
[GATE-2005]
- a)zero
- b)2.5 N
- c)5 N
- d)25N
Correct answer is option 'A'. Can you explain this answer?
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A simple pendulum of length 5 m, with a bob of mass 1 kg, is in simple...
Force at mean position is zero.
Most Upvoted Answer
A simple pendulum of length 5 m, with a bob of mass 1 kg, is in simple...
Solution:
Given, length of pendulum, L = 5 m
Mass of the bob, m = 1 kg
Speed of the bob, v = 5 m/s
Net force on the bob at mean position, F
We know that the equation of motion for a simple pendulum is given by:
T = 2π√(L/g)
Where T is the time period and g is the acceleration due to gravity.
Let us find the time period of the pendulum:
T = 2π√(L/g)
g = (2π/L)^2 * L/g
g = (4π^2)/L
g = 4π^2/5
T = 2π√(L/g)
T = 2π√(5/4π^2)
T = 2/π s
Now, let us find the amplitude of the pendulum:
At mean position, the velocity of the bob is maximum and the displacement is zero. So, the amplitude is given by:
A = vT/2π
A = 5*(2/π)/(2π)
A = 5/π m
Now, let us find the restoring force on the bob:
At any position, the restoring force on the bob is given by:
F = -mg*sin(θ)
Where θ is the angle made by the pendulum with the vertical.
At the mean position, θ = 0°
So, sin(θ) = sin(0) = 0
Therefore, the restoring force at the mean position is zero.
Hence, the net force on the bob at the mean position is zero.
Therefore, the correct option is (a).
Given, length of pendulum, L = 5 m
Mass of the bob, m = 1 kg
Speed of the bob, v = 5 m/s
Net force on the bob at mean position, F
We know that the equation of motion for a simple pendulum is given by:
T = 2π√(L/g)
Where T is the time period and g is the acceleration due to gravity.
Let us find the time period of the pendulum:
T = 2π√(L/g)
g = (2π/L)^2 * L/g
g = (4π^2)/L
g = 4π^2/5
T = 2π√(L/g)
T = 2π√(5/4π^2)
T = 2/π s
Now, let us find the amplitude of the pendulum:
At mean position, the velocity of the bob is maximum and the displacement is zero. So, the amplitude is given by:
A = vT/2π
A = 5*(2/π)/(2π)
A = 5/π m
Now, let us find the restoring force on the bob:
At any position, the restoring force on the bob is given by:
F = -mg*sin(θ)
Where θ is the angle made by the pendulum with the vertical.
At the mean position, θ = 0°
So, sin(θ) = sin(0) = 0
Therefore, the restoring force at the mean position is zero.
Hence, the net force on the bob at the mean position is zero.
Therefore, the correct option is (a).
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A simple pendulum of length 5 m, with a bob of mass 1 kg, is in simple harmonic motion as it passes through its mean position, the bob has a speed of 5 m/s. The net force on the bob at the mean position is[GATE-2005]a)zerob)2.5 Nc)5 Nd)25NCorrect answer is option 'A'. Can you explain this answer?
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