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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): When a car accelerates horizontally, the tension in the string of a suspended pendulum in equilibrium (relative to the car) is greater than its actual weight ( mg ). Reason (R): The effective acceleration due to gravity in the frame of the accelerating car is g^2 + a^2 , which is greater than g . I

Options

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

Correct answer

C. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

Step-by-step solution

In the frame of the accelerating car, the pendulum bob experiences a horizontal pseudo force ma in the direction opposite to the acceleration, in addition to the downward gravitational force mg . The net force acting on the bob in this non-inertial frame is F_ net = (mg)^2 + (ma)^2 = m g^2 + a^2 . Therefore, the effective acceleration due to gravity is g_ eff = g^2 + a^2 , which is strictly greater than g . To maintain equilibrium relative to the car, the tension T in the string must balance this net force. Thus, T

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