Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements. choose the most appropriate answer from the options given below:
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The time period of a simple pendulum is inversely related to the square root of the acceleration due to gravity.
Both (A) and (R) are true but (R) is not the correct explanation of (A)
(A) is false but (R) is true
Both (A) and (R) are true and (R) is the correct explanation of (A)
(A) is true but (R) is false
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The Correct Option isA
Solution and Explanation
To solve the problem, let's analyze the given statements:
Assertion (A): The time period of a simple pendulum is longer at the top of a mountain than at the base of the mountain.
Reason (R): The time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
The formula for the time period (T) of a simple pendulum is: T = 2π√(L/g) where L is the length of the pendulum and g is the acceleration due to gravity. From this formula, we see that the time period is inversely related to the square root of g. As the altitude increases, like at the top of a mountain, the value of g decreases slightly because of the increase in distance from the center of the Earth. This leads to a longer time period (T) at the mountain top compared to the base. Thus, Assertion (A) is true. The Reason (R) correctly states that the time period decreases with an increase in g, which is mathematically accurate. However, while this reason is true, it does not specifically explain why the time period is longer at a mountain top. This is due to the decrease in g at higher altitudes, which is only indirectly related to the reason given. Therefore, the correct answer is: Both (A) and (R) are true but (R) is not the correct explanation of (A).
