Class 11 Exam > Class 11 Questions > If length of pendulum is increased by 2%. The...
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If length of pendulum is increased by 2%. The time period will
- a)Increase by 1%
- b)Decrease by1%
- c)Increase by 2%
- d)Decrease by 2%
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If length of pendulum is increased by 2%. The time period willa)Increa...
Explanation:
When a pendulum swings, it completes one cycle back and forth in a certain amount of time. This time is called the period of the pendulum. The time period of a pendulum depends on the length of the pendulum, the acceleration due to gravity, and the angle through which the pendulum swings.
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.
Now, let's see how the time period of a pendulum changes when the length of the pendulum is increased by 2%.
When the length of the pendulum is increased by 2%:
New length of the pendulum = 1.02L (where L is the original length of the pendulum)
New time period of the pendulum = 2π√(1.02L/g)
To find the percentage change in the time period, we can use the formula:
% Change = (New Value - Old Value)/Old Value x 100
% Change = ((2π√(1.02L/g)) - (2π√(L/g)))/(2π√(L/g)) x 100
% Change = (√(1.02) - 1) x 100
% Change = 0.994 x 100
% Change = 0.994%
Therefore, the time period of the pendulum increases by 0.994%, which is approximately 1%. Hence, the correct option is A.
When a pendulum swings, it completes one cycle back and forth in a certain amount of time. This time is called the period of the pendulum. The time period of a pendulum depends on the length of the pendulum, the acceleration due to gravity, and the angle through which the pendulum swings.
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.
Now, let's see how the time period of a pendulum changes when the length of the pendulum is increased by 2%.
When the length of the pendulum is increased by 2%:
New length of the pendulum = 1.02L (where L is the original length of the pendulum)
New time period of the pendulum = 2π√(1.02L/g)
To find the percentage change in the time period, we can use the formula:
% Change = (New Value - Old Value)/Old Value x 100
% Change = ((2π√(1.02L/g)) - (2π√(L/g)))/(2π√(L/g)) x 100
% Change = (√(1.02) - 1) x 100
% Change = 0.994 x 100
% Change = 0.994%
Therefore, the time period of the pendulum increases by 0.994%, which is approximately 1%. Hence, the correct option is A.
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Community Answer
If length of pendulum is increased by 2%. The time period willa)Increa...
In this question , The formula for time period - T = 2π√L/g = 2π (L/g)^1/2 2,π,g have no dimensions ∆T/T = 1/2 x ∆L/L By representing in percentage error ∆T/T x 100 = 1/2 x ∆L/L x 100 ∆T/T % = 1/2 x 2 % ∆T/T % = 1 % the time period becomes 1 %
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