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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The angular speed of the hour hand of a clock is half the angular speed of the Earth's rotation about its own axis. Reason (R): The hour hand completes one revolution in 12 hours, whereas the Earth completes one revolution in 24 hours. In the light of the above statements, choose the most appropria

Options

  1. ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
  2. BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
  3. CAssertion (A) is true but Reason (R) is false
  4. DAssertion (A) is false but Reason (R) is true

Correct answer

D. Assertion (A) is false but Reason (R) is true

Step-by-step solution

The time period of the hour hand of a clock is T_H = 12 hours . The time period of the Earth's rotation about its own axis is T_E = 24 hours . Angular speed is given by = 2 T . Therefore, _H = 2 12 and _E = 2 24 . Taking the ratio, _H _E = 24 12 = 2 . Thus, the angular speed of the hour hand is twice that of the Earth's rotation, making the Assertion (A) false. The Reason (R) correctly states the respective time periods, so it is true. Answer: Assertion (A) is false but Reason (R) is true

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