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A : If angular speed of the earth incre...

A : If angular speed of the earth increases , the effective g will decrease at all places on earth .
R: The value of 'g ' at latitude `lambda` is given by ` g ' = g - omega^(2)Rcos^(2)lambda`

A

If both Assertion & Reason are true . And the reason is the correct explanation of the assertion , then mark (1)

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2)

C

If Assertion is true statement but Reason is false , then mark (3)

D

If Assertion is false statement but Reason is true then, mark (4)

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the assertion (A) and the reason (R) provided in the question regarding the effect of the Earth's angular speed on the effective acceleration due to gravity (g'). ### Step-by-Step Solution: 1. **Understand the Assertion (A)**: - The assertion states that if the angular speed of the Earth increases, the effective g will decrease at all places on Earth. - We need to confirm whether this statement is true. 2. **Understand the Reason (R)**: - The reason states that the value of 'g' at latitude λ is given by the formula: \[ g' = g - \omega^2 R \cos^2 \lambda \] - Here, \(g\) is the standard acceleration due to gravity, \(\omega\) is the angular speed of the Earth, \(R\) is the radius of the Earth, and \(\lambda\) is the latitude. 3. **Analyze the Formula**: - The formula shows that the effective gravity \(g'\) is equal to the standard gravity \(g\) minus a term that depends on the angular speed \(\omega\). - The term \(\omega^2 R \cos^2 \lambda\) represents the centrifugal effect due to the Earth's rotation, which reduces the effective gravity. 4. **Effect of Increasing Angular Speed**: - If the angular speed \(\omega\) increases, the term \(\omega^2 R \cos^2 \lambda\) also increases. - This means that the subtraction from \(g\) becomes larger, leading to a decrease in \(g'\). 5. **Conclusion about Assertion (A)**: - Since increasing \(\omega\) results in a larger subtraction from \(g\), it confirms that the effective gravity \(g'\) decreases at all places on Earth. - Therefore, the assertion (A) is true. 6. **Conclusion about Reason (R)**: - The reason (R) correctly explains how \(g'\) is calculated and is indeed true. - The formula provided is accurate and directly relates to the assertion. 7. **Final Answer**: - Both the assertion and the reason are true, and the reason is the correct explanation of the assertion. Therefore, the correct option is that both A and R are true, and R is the correct explanation of A.
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