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A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :
- a)α
- b)α/2
- c)2α
- d)1/α
Correct answer is option 'B'. Can you explain this answer?
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A simple pendulum made of a bob of mass m and a metallic wire of negli...
Assuming that the pendulum is undergoing small oscillations, we can use the formula for the time period of a simple pendulum:
T = 2π√(l/g)
where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.
At T=0, we know that the time period is 2 seconds. Therefore, we can write:
2 = 2π√(l/g)
Squaring both sides, we get:
4 = 4π^2(l/g)
Dividing both sides by 4π^2, we get:
l/g = 1/π^2
Rearranging, we get:
l = g/π^2
Now, we can use this value of l to find the length of the pendulum required for a time period of 1 second:
1 = 2π√(l/g)
Squaring both sides and substituting the value of l, we get:
1 = 4π^2(g/π^2)/g
Simplifying, we get:
1 = 4π^2/π^2
Therefore, the length of the pendulum required for a time period of 1 second is:
l = g/π^2 = 9.81/π^2 meters
Note that this calculation assumes that the amplitude of the oscillations is small enough that the pendulum can be considered a simple harmonic oscillator. If the amplitude is too large, the pendulum's motion may become nonlinear and the time period may be different than what is predicted by this formula.
T = 2π√(l/g)
where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.
At T=0, we know that the time period is 2 seconds. Therefore, we can write:
2 = 2π√(l/g)
Squaring both sides, we get:
4 = 4π^2(l/g)
Dividing both sides by 4π^2, we get:
l/g = 1/π^2
Rearranging, we get:
l = g/π^2
Now, we can use this value of l to find the length of the pendulum required for a time period of 1 second:
1 = 2π√(l/g)
Squaring both sides and substituting the value of l, we get:
1 = 4π^2(g/π^2)/g
Simplifying, we get:
1 = 4π^2/π^2
Therefore, the length of the pendulum required for a time period of 1 second is:
l = g/π^2 = 9.81/π^2 meters
Note that this calculation assumes that the amplitude of the oscillations is small enough that the pendulum can be considered a simple harmonic oscillator. If the amplitude is too large, the pendulum's motion may become nonlinear and the time period may be different than what is predicted by this formula.
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A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer?
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A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer?.
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