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NEETPhysicsMotion in Two Dimensions

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If two particles move in circular paths of different radii with the same uniform linear speed, the particle on the smaller circle experiences a greater centripetal acceleration. Reason (R): The time period of a particle in uniform circular motion is directly proportional to its radius and inversely

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

B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)

Step-by-step solution

Assertion (A) is true: The centripetal acceleration is given by a_c = v^2 r . For a constant linear speed v , a_c 1 r . Thus, a smaller radius r results in a greater centripetal acceleration. Reason (R) is true: The time period is given by T = 2 r v . This shows that T is directly proportional to r and inversely proportional to v . However, Reason (R) does not explain Assertion (A). The correct explanation for the assertion is the inverse relationship between centripetal acceleration and radius for a given speed, n

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