Correct option is D
Given:
- Three strips of 10 m width each are placed along:
- Equator (A1)
- Tropic of Cancer (A2)
- Arctic Circle (A3)
- All strips have equal width but are located at different positions on the Earth's surface.
Concept Used:
The Earth is approximately spherical. The circumference of a circle decreases as we move from the equator (θ = 0°) to the poles (θ increases).
Area of a strip = Width × Circumference at angle θ
Formula Used:
Circumference at angle θ = 2πR cos(θ)
As θ increases, cos(θ) decreases, so the circumference and area of the strip also decrease.
Solution:
- At θ = 0° (Equator), cos(θ) = 1 → Maximum circumference → Maximum area (A1)
- At θ = 23.5° (Tropic of Cancer), cos(θ) is slightly less → Smaller area (A2)
- At θ = 66.5° (Arctic Circle), cos(θ) is much smaller → Smallest area (A3)
Therefore, the relationship is:
A1 > A2 > A3
Correct Option: (D) A1 > A2 > A3
