A bead P sliding on a frictionless semi-circular string... bead Q ejected... relation between and is

- A
- B
- C
- D
A bead P sliding on a frictionless semi-circular string... bead Q ejected... relation between and is

Correct answer:D
Standard Method
Given: Bead P slides on a frictionless semicircular string, while bead Q is ejected. We need to compare the times and .
Find: The correct relation between and .
From the extracted solution: bead Q moves with constant speed .
Bead P accelerates due to gravity along the curved path, so its average speed becomes greater than .
Although bead P travels along a longer path, the increase in speed makes its travel time smaller.
Therefore, . The correct option is D.
Assuming the shorter geometric path must always take less time. This is wrong because time depends on both path length and speed. Here bead P gains speed due to gravity, so compare travel time, not only distance.
Treating both beads as moving with the same constant speed. This is wrong because only bead Q moves with constant speed , while bead P accelerates on the curved path. Use the change in speed for bead P.
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