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NEETPhysicsLaws of Motion

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The maximum horizontal acceleration a trolley can have without a block slipping on its floor is independent of the mass of the block. Reason (R): The limiting static friction force between the block and the trolley floor is independent of the mass of the block. In the light of the above statements,

Options

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

Correct answer

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

Step-by-step solution

In the non-inertial frame of the accelerating trolley, a pseudo force F_p = ma acts on the block of mass m in the direction opposite to the acceleration a . The limiting static friction force opposing this tendency to slip is f_ s, max = _s N = _s mg . For the block not to slip, the pseudo force must be less than or equal to the limiting static friction: ma _s mg a _s g The maximum acceleration is a_ max = _s g , which is independent of the mass m of the block. Therefore, Assertion (A) is true. The limiting static

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