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If the length of a simple pendulum is increased by 2%, then the time period [1997]
- a)increases by 2%
- b)decreases by 2%
- c)increases by 1%
- d)decreases by 1%
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the length of a simple pendulum is increased by 2%, then the time p...
T=2π√l/g
here we take g=constant..
so T Will b proportional to √l....
for small change in length
ΔT/T=1/2Δl/l
=1/2(2%)
=1% increase (since it is directly proportional)
here we take g=constant..
so T Will b proportional to √l....
for small change in length
ΔT/T=1/2Δl/l
=1/2(2%)
=1% increase (since it is directly proportional)
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Community Answer
If the length of a simple pendulum is increased by 2%, then the time p...
Explanation:
When the length of a simple pendulum is increased, the time period of the pendulum also changes. The time period of a simple pendulum is the time taken for one complete oscillation, i.e., the time taken for the pendulum to swing from one extreme to the other and back again.
Relationship between time period and length of a simple pendulum:
The time period of a simple pendulum is given by the 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.
Effect of increasing the length of the pendulum:
When the length of the pendulum is increased, the time period also increases. This can be understood by analyzing the formula for the time period.
Analyzing the formula:
If we increase the length of the pendulum by 2%, it means the new length becomes 1.02 times the original length.
Therefore, the new length (L') can be expressed as:
L' = 1.02L
Substituting the new length into the formula:
T' = 2π√(L'/g)
= 2π√((1.02L)/g)
= 2π√((1.02/g) * L)
= (1.02/g) * 2π√(L)
Comparing the new time period with the original time period:
We can see that the new time period (T') is equal to (1.02/g) times the original time period (T).
Therefore, the new time period is increased by a factor of 1.02/g compared to the original time period.
Conclusion:
Since the acceleration due to gravity (g) remains constant, the new time period (T') is increased by a factor of 1.02 compared to the original time period (T). This corresponds to an increase of 1% in the time period.
Hence, the correct answer is option C) increases by 1%.
When the length of a simple pendulum is increased, the time period of the pendulum also changes. The time period of a simple pendulum is the time taken for one complete oscillation, i.e., the time taken for the pendulum to swing from one extreme to the other and back again.
Relationship between time period and length of a simple pendulum:
The time period of a simple pendulum is given by the 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.
Effect of increasing the length of the pendulum:
When the length of the pendulum is increased, the time period also increases. This can be understood by analyzing the formula for the time period.
Analyzing the formula:
If we increase the length of the pendulum by 2%, it means the new length becomes 1.02 times the original length.
Therefore, the new length (L') can be expressed as:
L' = 1.02L
Substituting the new length into the formula:
T' = 2π√(L'/g)
= 2π√((1.02L)/g)
= 2π√((1.02/g) * L)
= (1.02/g) * 2π√(L)
Comparing the new time period with the original time period:
We can see that the new time period (T') is equal to (1.02/g) times the original time period (T).
Therefore, the new time period is increased by a factor of 1.02/g compared to the original time period.
Conclusion:
Since the acceleration due to gravity (g) remains constant, the new time period (T') is increased by a factor of 1.02 compared to the original time period (T). This corresponds to an increase of 1% in the time period.
Hence, the correct answer is option C) increases by 1%.
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If the length of a simple pendulum is increased by 2%, then the time period [1997]a)increases by 2%b)decreases by 2%c)increases by 1%d)decreases by 1%Correct answer is option 'C'. Can you explain this answer?
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