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Q3.10: NCERT Physics - Part 1 MOTION IN A PLANE 3.10 Solution: On an open ground, a motorist follows a track that turns to his …
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often equate the total distance travelled (3 × 500 m, 6 × 500 m, etc.) with the straight‑line displacement, ignoring that each 60° turn changes direction. The correct approach is to add the 500 m vectors head‑to‑tail as sides of a regular hexagon; after three turns the resultant is the chord of two sides (1000 m), after six turns the vectors close the hexagon giving zero displacement, and after eight turns the resultant is the side plus the next chord (500√3 m).
On an open ground, a motorist follows a track that turns to his left by an angle of 60� after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
Step-by-Step Verified Solution
**Answer:** Third turn: 1000 m, path 1500 m. Sixth turn: 0, path 3000 m. Eighth turn: 500�3 m, path 4000 m.
**Step-by-Step Explanation:**
The path forms a regular hexagon (turns of 60�).
Third turn: displacement = 2 _ 500 = 1000 m (two sides of hexagon).
Sixth turn: displacement = 0 (returns to start).
Eighth turn: displacement = 500�3 m (two turns after completing hexagon).
Path lengths: 3 _ 500 = 1500 m; 6 _ 500 = 3000 m; 8 _ 500 = 4000 m.
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