A block is released from rest at a height on a smooth curved track. At the bottom it crosses a rough horizontal patch of length (), then compresses a light spring of constant on a smooth surface, rebounds, crosses the rough patch again and climbs the smooth track. Taking , the height it reaches on the return is

Answer and explanation

Correct answer: A.

  1. Step 1: Compute the block's initial mechanical energy: .
  2. Step 2: Determine the work dissipated by friction on each crossing of the rough patch: .
  3. Step 3: Because the block traverses the rough patch twice (once moving toward the spring, and once rebounding back), total dissipated energy is .
  4. Step 4: The remaining mechanical energy is . Re-climbing the track yields final height .
Answer
.
Why not the others: accounts for only a single crossing of the rough friction section.

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