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Two identical simple pendulums are used as clocks. Clock-1 sits on Earth's surface and Clock-2 is at a height h above the surface. Their measured time periods are 4 s and 6 s respectively. Taking Earth's radius R_E = 6400 km, find h.

1. 1200 km
2. 1600 km
3. 3200 km
4. 4800 km

Correct answer: 3200 km

Solution

Since T proportional to 1/sqrt(g) and g(h) = g*(R/(R+h))², we get T2/T1 = sqrt(g/g(h)) = (R+h)/R. So 6/4 = (R+h)/R => 1 + h/R = 1.5 => h = 0.5*R = 0.5*6400 = 3200 km.

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